Excerpt

## Table of Contents

Abstract

Résumé

Riassunto

Abbreviations and acronyms

1. Introduction

1.1 Changes in the Mean Ruminal pH Profile of Beef Cattle during Acidosis

1.2 Mathematical Modelling in Animal Nutrition

1.2.1 Prediction of the Mean Ruminal pH from Dietary Compositions

1.2.1.1 Mertens, (1986-1997)

1.2.1.2 Cornell Net Carbohydrate Protein System, (1992-2008)

1.2.1.3 Zebeli et al. (2006) and (2008) models

1.2.2 Prediction of the Mean Ruminal pH from Ruminal Fermentation end-products

1.2.2.1 Tamminga and Van Vuuren, (1988)

1.2.2.2 Institut National de la Recherche Agronomique, (1995)

1.2.2.3 Allen, (1997)

2. Materials and Methods

2.1 Database Compilation

2.2 Database Description

2.3 Dietary Compositions and Missing Values

2.4 Ruminal Fermentation Characteristics and Calculations

2.5 Extant Prediction Equations

2.6 Development of new prediction equations

2.7 Models adequacy and evaluation

2.8 Residual analysis

3. Results

3.1. Descriptive Statistics of Literature Data

3.2. Correlation Analyses of Literature Data

3.3. Development of mean Rumen pH prediction models from all of the pH measurements observations

3.4. Development of mean Rumen pH prediction models from continuously measured observations

3.5. Evaluation of extant Rumen pH prediction models

3.5.1 Performance of the tested models against all the different rumen pH measurements.observations

3.5.2 Performance of the tested models against continuously measured rumen pH observations

4. Discussion

4.1. Ruminal pH Prediction from the extant published models

4.2 Use of ruminal fermentation characteristics (VFA) in mean Ruminal pH Prediction

4.3 Use of dietary composition and ruminal variables in mean Ruminal pH Prediction

4.4 Recommended Equations for prediction of mean Rumen pH for beef cattle

4.5 Recommendations for Further Research

5. Conclusion

6. Appendix

6.1. List of Tables

Table 1. Comparison of acute and sub-acute acidosis in beef cattle

Table 2. Main Factors affecting ruminal acidosis in beef cattle

Table 3. Factors affecting ruminal pH in beef cattle

Table 4. Descriptive statistics of database (1)

Table 5. Descriptive statistics of database (2)

Table 6. Summary of database (1) used to evaluate the performance of the published ruminal pH prediction models and for the modulation of new ruminal pH prediction equations from the different published ruminal pH measurement techniques

Table 7. Summary of database (2) used to evaluate the performance of the published ruminal pH prediction models and for the modulation of new ruminal pH prediction equations from the different published ruminal pH measurement techniques

Table 8. Publications included in the database used in modeling the ruminal pH from *in-vivo* beef cattle measurements

Table 9. Description of dataset assembled from different studies categorized into: Author, location of study, type of study, main grain type in the diet, and diet type

Table 10. Description of dataset assembled from different studies categorized into: main ingredients in diets, initial bodyweight and average body weight

Table 11. Description of dataset assembled from different studies categorized into: treatment description and diets compositions (Forage, CP, NDF, peNDF, and predicted peNDF from Pitt *et al.* (1996), Mertenes (1996), Zebeli *et al.* (2008), and Fox *et al.* (2004) equations

Table 12. Description of dataset assembled from different studies categorized into: the animal pH sampling method; post-feeding times; DMI; and dietary compositions of the diets (ADF, NDF, Forage NDF, Lignin, NFC, Sugar, Starch, SS, EE, and Ash)

Table 13. Description of the dataset assembled from different studies categorized into: predicted RpH from (Lescoat and Sauvant, 1995, LES; Pitt *et al.*, 1996, PIT; Tamminga and Van Vuuren, 1988, TAM; Fox et al., 2004, FOX; and Zebeli *et al.*, 2008, ZB8; observed mean RpH, minimum (nadir) RpH; time RpH < 5.2 (h); time RpH < 5.5 (h); time RpH < 5.6 (h); time RpH < 5.8 (h); total VFA, tVFA (mM); molar percentage of Acetate, AC; Propionate, PR; Butyrate, BU; and Ammonia, Am (mM) concentration

Table 14. Description of the dataset assembled from different studies categorized into: dietary intake (% kg d-^{1} ) of Forage, DM, CP, ADF, peNDF, peNDF from Pitt *et al.* (1996), Fox *et al*. (2004) and Mertenes (1996) equations, NDF, Forage NDF, Lignin, Sugar, Starch, SS, EE and Ash

Table 15.1. Across-study linear relationship for the animal response to ruminal pH from database (1) variables

Table 15.2. Across-study quadratic relationship for the animal response to ruminal pH from database (1) variables

Table 15.3. Across-study cubic relationship for the animal response to ruminal pH from database (1) variables

Table 15. 4. Across-study (linear, cubic, and quadratic) relationships for the animal response to ruminal pH from database (1) variables

Table 15.5 .Pearson's correlation between measured ruminal pH, rumen fermentation characteristics, and dietary compositions (kg/d)

Table 16. Summary of the best simple linear and polynomial relationships described the mean ruminal pH observed from the database variables

Table 16. 1. Across-study (linear, cubic, and quadratic) relationships for the animal response to ruminal pH from database (2) variables

Table 16.2. Positive Pearson’s correlation between measured mean ruminal pH and dietary proportion (%) and intake (kg/d) and ruminal fermentation

Table 16.3. Negative Pearson's correlation between measured mean ruminal pH and dietary proportion (%) and intake (kg/d) and ruminal fermentation

Table 17. Performance of models developed from database (1) for mean ruminal pH predictions ranked with the highest CCC

Table 17.2. Performance of models developed from database (1) for mean ruminal pH predictions ranked with the highest CCC

Table 17.4. Evaluation of the tested models developed from database (1) for prediction biases of mean ruminal pH in beef cattle

Table 18. Performance of models developed from database (2) for mean ruminal pH predictions ranked with the highest CCC

Table 18.1. Performance of models developed from database (2) for mean ruminal pH predictions ranked with the lowest RMSPE

Table 18.2. Performance of models developed from database (2) for mean ruminal pH predictions ranked with the highest CCC

Table 18.3. Performance of models developed from database (2) for mean ruminal pH predictions ranked with the lowest RMSPE

Table 18.4. Evaluation of the tested models developed from database (2) for prediction biases of mean ruminal pH in beef cattle

Table 19. Comparative evaluation of ruminal pH prediction models ranked with the highest CCC

Table 19.1. Comparative evaluation of ruminal pH prediction models ranked with the lowest RMSPE

Table 19.2. Comparative evaluation of ruminal pH prediction models ranked with the highest CCC

Table 19.3. Comparative evaluation of ruminal pH prediction models ranked with the lowest RMSPE

Table 19.4. Evaluation of the tested extant models for prediction biases of mean ruminal pH in beef cattle

6.2. List of Figures

Figure 1. Observed *versus* predicted mean rumen pH of the best fit equations describing the mean rumen pH from uncontinuously measured techniques for [Eq. (A), (B), (C), and (D)], applied on database (1) and (2). Predictions from Eq. (A) were assigned for total VFA (m *M*); propionate-quadratic (%) and butyrate-quadratic (%). Predictions from Eq. (B) were based on starch-quadratic (kg/d, DM); propionate- quadratic (%) and butyrate-quadratic (%). Predictions from Eq. (C) were based on forage NDF (kg/d, DM); NFC (kg/d, DM) and Lignin-quadratic (kg/d, DM). Predictions from Eq. (D) were based on DMI (Kg/d, DM) and ADF (% diet DM)

Figure 2. Residuals *versus* centered predicted mean rumen pH for [Eq (A), (B), (C), and (D)], applied on database (1) and (2). The independent variable (predicted mean rumen pH) was centered on the mean predicted value before the residuals were regressed on the predicted values by subtracting the mean of all predicted values from each predicted value. Prediction from Eq. (A) were assigned for total VFA (m *M*); propionate-quadratic (%) and butyrate-quadratic (%). Prediction from Eq. (B) were based on starch- quadratic (kg/d, DM); propionate-quadratic (%) and butyrate-quadratic (%). Prediction from Eq.(C) were based on forage NDF (kg/d, DM); NFC (kg/d, DM) and Lignin-quadratic (kg/d, DM). Prediction from Eq. (D) were based on DMI (Kg/d, DM) and ADF (% diet DM)

Figure 3. Observed *versus* predicted mean rumen pH of the best fit equations describing the mean rumen pH from continuously measured techniques based on VFA predictions from [Eq. (F) and (G)], applied on database (1) and (2). Eq. (F) included ruminal ammonia-cubic concentrations (m *M*) and acetate-cubic (%). A prediction from Eq. (G) was based on acetate-cubic (%)

Figure 3.1. Residuals *versus* centered predicted mean rumen pH of the best fit equations describing the mean rumen pH from continuously measured techniques based on VFA predictions from [Eq (F) and (G)], applied on database (1) and (2). Predicted mean rumen pH was centered on the mean predicted value before the residuals were regressed on the predicted values by subtracting the mean of all predicted values from each predicted value. Eq. (F) included ruminal ammonia-cubic concentrations (m *M*) and acetate-cubic (%). A prediction from Eq. (G) was based on acetate-cubic (%)

Figure 3.2. Observed *versus* predicted mean rumen pH of the best fit equations describing the mean rumen pH from continuously measured techniques based on VFA and dietary intake predictions from [Eq. (I)], applied on database (1) and (2). Eq. (I) included forage (kg/d % diet DM), butyrate (%) and ruminal ammonia (m *M*)

Figure 3.3. Residuals *versus* centered predicted mean rumen pH of the best fit equations describing the mean rumen pH from continuously measured techniques based on VFA and dietary intake predictions from [Eq. (I)], applied on database (1) and (2). Eq. (I) included forage (kg/d % diet DM), butyrate (%) and ruminal ammonia.(m *M*)

Figure 3.4. Observed *versus* predicted mean rumen pH of the best fit equations describing the mean rumen pH from continuously measured techniques based on VFA and dietary compositions predictions from [Eq. (E) and (L)], applied on database (1) and (2). Eq. (E) included forage forage (% diet DM), OM (% diet DM), and ammonia (m *M*). Predictions from Eq. (L) included peNDF (% diet DM), starch (% diet DM), and acetate (%). Predictions from Eq. (L) were based on peNDF (% diet DM), starch (% diet DM) and acetate (%)

Figure 3.5. Residuals *versus* centered predicted mean rumen pH of best fit equations describing mean rumen pH from continuously measured techniques based on VFA and dietary compositions predictions from [Eq. (E) and (L)], applied on database (1) and (2). Eq. (E) included forage forage (% diet DM), OM (% diet DM), and ammonia (m *M*). Predictions from Eq. (L) included peNDF (% diet DM), starch (% diet DM), and acetate (%). Predictions from Eq. (L) were based on peNDF (% diet DM), starch (% diet DM) and acetate (%)

Figure 3.6. Observed *versus* predicted mean rumen pH of the best fit equations describing mean rumen pH from continuously measured techniques based on dietary intake predictions from [Eq. (J) and (K)], applied on database (1) and (2). Eq. (J) included EE (kg/d % diet DM), forage-quadratic (kg/d % diet DM), and sugar-quadratic (kg DM/d). Predictions from Eq. (K) included forage (kg/d % diet DM)

Figure 3. Residuals *versus* centered predicted mean rumen pH of the best fit equations describing mean rumen pH from continuously measured techniques based on dietary intake predictions from [Eq. (J) and (K)], applied on database (1) and (2). Eq. (J) included EE (kg/d % diet DM), forage-quadratic (kg/d % diet DM), and sugar-quadratic (kg/d % diet DM). Predictions from Eq. (K) included forage (kg/d % diet DM)

Figure 3.8. Residuals *versus* centered predicted mean rumen pH of the best fit equations describing the mean rumen pH from continuously measured techniques based on dietary intake predictions from [Eq. (H) and (M)], applied on database (1) and (2). Eq. (H) included forage (% diet DM). Predictions from Eq. (M) included peNDF and starch (% diet DM)

Figure 3.9. Residuals *versus* centered predicted mean rumen pH of the best fit equations describing the mean rumen pH from continuously measured techniques based on dietary intake predictions from [Eq. (H) and (M)], applied on database (1) and (2). Eq. (H) included forage (% diet DM). Predictions from Eq. (M) included peNDF and starch (% diet DM)

Figure 3.10. Observed *versus* predicted mean rumen pH of the best fit equations describing the mean rumen pH from continuously measured techniques based on dietary intake predictions from [Eq. (N), (O), and (P)], applied on database (1) and (2). Eq. (N) included peNDF (% diet DM). Predictions from Eq. (O) included NDF (% diet DM). Predictions from Eq. (P) included NDF- and starch- (quadratic, % diet DM)

Figure 3.11. Residuals *versus* centered predicted mean rumen pH of the best fit equations describing the mean rumen pH from continuously measured techniques based on dietary intake predictions from [Eq. (N), (O), and (P)], applied on database (1) and (2). Eq. (N) included peNDF (% diet DM). Predictions from Eq. (O) included NDF (% diet DM). Predictions from Eq. (P) included NDF- and starch- (quadratic, % diet DM)

Figure 4. Observed *versus* predicted mean rumen pH for VFA-based models of Tamminga and Van Vuuren (1988), Lescoat and Sauvant (1995) and ALL, Allen (1997) equations, applied on database (1) and (2) where predictions were assigned for total VFA concentrations

Figure 4.1. Residuals *versus* centered predicted mean rumen pH for VFA-based models of Tamminga and VanVuuren (1988), Lescoat and Sauvant (1995) and Allen (1997) equations, applied on database (1) and (2) where predictions were assigned for total ruminal VFA concentrations

Figure 4.2. Observed versus predicted mean rumen pH for peNDF-beef based models of Fox *et al.* (2004) and Pitt *et al.* (1996); equations, applied on database (1) and (2) where predictions were assigned for physical effective fiber

Figure 4.3. Observed versus predicted mean rumen pH for peNDF-beef based models of Fox *et al. * (2004) and Pitt *et al*. (1996) equations, applied on database (1) and (2) where predictions were assigned for the dietary physical effective fiber

Figure 4.4. Observed versus predicted mean rumen pH for peNDF-Dairy based models of Mertens (1997), Zebeli *et al.* (2006) and Zebeli *et al*. (2008) equations, applied on database (1) and (2) where predictions were assigned for the dietary physical effective fiber

Figure 4.5. Observed versus predicted mean rumen pH for peNDF-Dairy based models of Mertens (1997), Zebeli *et al.* (2006) and Zebeli *et al.* (2008) equations, applied on database (1) and (2) where predictions were assigned for the dietary physical effective fiber

7. References

7.1. Experiments used in the Meta-Analysis and Listed in Appendix (Tables 8-14)

7.2. Literature cited

8. Acknowledgement

## Abstract

Sarhan, M., 2014. *Prediction of Ruminal pH for Beef Cattle: A Physiological Modelling Approach. M.Sc. Thesis, Catania University (DISPA), Italy and Montpellier SupAgro (PARC), France*

Ruminal fluid pH (RpH) is an important parameter for controlling the rumen functions. The ability to predict the RpH of beef cattle fed a given diet without depending on the invasive techniques for its measurements (*i.e.,* rumen cannula) is important to avoid ruminal acidosis. The objectives of this research were to: (i) identify key variables that have a significant associations with RpH; (ii) collect data points (DB) from *in-vivo* beef cattle studies to identify suitable predictors of RpH after considering the animal measures and the dietary variables from a wide range of diets that can safely be fed to beef cattle; (iii) evaluate the extant RpH models relevant to the study; and (iv) develop a new statistical models for mean RpH predictions. Therefore, feed additives (*i.e.,* monensin) were excluded from the analysis. Models tested that use physically effective fiber (peNDF) as a dependent variable were Pitt *et al*. (1996, PIT), Mertens (1997, MER), Fox *et al*. (2004, FOX), Zebeli *et al*. (2006, ZB6), and Zebeli *et al*. (2008, ZB8), and those that use rumen volatile fatty acids (VFAs) were Tamminga and Van Vuuren (1988, TAM), Lescoat and Sauvant (1995, LES), and Allen (1997, ALL). The final database was categorized into DB (1) and (2) that included a total of 232 and 95 treatment means from 65 and 26 peer-reviewed publications, respectively, spanning from the 1969s to 2014. The DB included information on animal characteristics, ration composition, and ruminal fermentation and pH, that has been used for independent evaluation and development of RpH prediction models. Missing values not reported by the authors were calculated using the sub- model Cornell Penn Minor Dairy model (CPM-Dairy©; version 3.0, Boston *et al.,* 2000) of the Cornell Net Carbohydrate and Protein System (CNCPS; version 4.0, Fox *et al*., 1992; Sniffen *et al*., 1992; O’Connor *et al*., 1993). The average bodyweight was 437±168 *vs.* 556±114 kg, dry matter intake (DMI) was 8.57±2.62 *vs.* 9.60±2.10 kgd-^{1}, peNDF (% DM) was 20.3±17.0 *vs.* 17.2±14.6, and forage (% DM) was 34.8±36.1 *vs.* 26.9±31.0 for DB (1) and (2), respectively. The cattle used were of various ages (*i.e.,* calves, yearlings, mature) and represented various production systems (*i.e.,* backgrounding, finishing, and zero-grazing). RpH across the studies was positively (*P* < 0.01) related to the dietary forage, acid detergent fiber (ADF), peNDF, neutral detergent fiber (NDF), forage NDF, lignin, sugar, ash, and ruminal concentrations of acetate (AC) and ammonia (Am) (r = 0.200-0.680 *vs.* 0.400-0.885) in DB (1) and (2), respectively. RpH was negatively correlated (*P* < 0.01) to DMI, propionate (PR), and starch (correlation of -0.330 to -0.750), and between total VFAs and organic matter (OM, *P* < 0.05) for DB (1) and DB (2) with the exception of non-structural carbohydrates (NFC), as well as metabolic DMI (*P* < 0.01) with a correlation between -0.274 to -0.851. Thus, ruminal [total VFAs, (m *M*), (PR, %), butyrate (BU, %), (AC, %) and (Am, m *M*)] and dietary variables (% DM basis) [DMI, ether extract, lignin, forage proportion, forage NDF, NFC, OM, sugar, peNDF, and starch] were considered in the development of mean RpH prediction models from DB (1) and (2). The main difference between the data sets was in how RpH had been measured. Ruminal pH measurements (RpHms) was broadly classified as continuous that use indwelling submersible pH electrodes or non-continuous described by sampling the rumen fluid once or at timed intervals. Both of RpHms were assigned for DB (1) whereas; only continuous RpHms were included in DB (2). Prediction equations were derived using the mixed model regression analysis, with a random effect for the study and fixed effect for the trials. The cross-validation (CV) approach was used to evaluate the new prediction equations. Assessments of models adequacy were performed as described in Tedeschi (2006). The Akaike's information criterion (AICc), the Bayesian information criterion (BIC), coefficient of model determination (CD), concordance correlation coefficient (CCC), modeling efficiency (MEF), root mean square error (RMSE), mean square prediction error (MSPE), root MSPE (RMSPE), and multiple coefficient of determination (R^{2} ) were used to determine variables of the best-fit-equations, and to evaluate the predictability of equations developed in the CV analysis. Mean centered and linear biases of prediction were also determined (St-Pierre, 2003). The following 4 best-fit-equations resulted in the lowest RMSPE, the highest CCC and MEF, moderate CD, and explained (0.44 to 0.82) of the variations in RpH from the total of the 16 newly developed models tested on DB (1) and (2). The linear Eq. (E): RpH = 3.32 (± 0.96) + 0.09 (± 0.004) × forage (% diet DM) + 0.02 (± 0.01) × OM (% diet DM) + 0.006 (± 0.003) × Am (m *M*) [AiCc = 7.81, BIC = 17.4, RMSE = 0.24, R^{2} = 0.90]; the cubic Eq. (F): RpH = 5.36 (± 0.04) + 3.48 × 10-^{6} (±2.26 × 10-^{7} ) × AC^{3} (mol/100 mol) + 3.76 × 10-^{5} (±1.47 × 10-^{5} ) × Am^{3} (m *M*) [AiCc = 40.4, BIC = 48.0, RMSE = 0.32, R^{2} = 0.80]; the cubic Eq. (G): RpH = 5.43 (± 0.04) + 3.37 × 10-^{6} (± 2.287 × 10-^{7} ) × AC^{3} (mol/100mol) and linear Eq. (H): RpH = 5.72 (± 0.018) + 0.009 (± 0.0005) × forage (% diet DM) [AiCc = 71.9, BIC = 79.3, RMSE = 0.34, R[2] = 0.78]. The magnitude of these models performance after evaluation on DB (1) and (2), respectively, was as follows. For Eq. (F): CCC of 0.64 *vs.* 0.90, CD of 1.21 *vs.* 1.55, MEF of 0.37 *vs.* 0.81 and RMSPE of 2.18 *vs.* 5.34% with (94.9 to 99.6% of MSPE) errors from random sources. For Eq. (H): (CCC of 0.61 *vs.* 0.90), (CD of 1.16 *vs.* 1.60), (MEF of 0.37 *vs.* 0.81), and RMSPE of 2.24 *vs.* 5.56% and 98.5 *vs.* 99.4% of which was random error. For Eq. (G): CCC of 0.64 *vs.* 0.87, CD of 1.27 *vs.* 1.79, MEF of 0.43 *vs.* 0.77, and RMSPE of 2.38 *vs.* 5.32% with (98.5 to 99.4% of MSPE) errors from random sources. For Eq. (E): CCC of 0.55 *vs.* 0.90, CD of 1.1 *vs.* 1.48, MEF of 0.25 *vs.* 0.82, and RMSPE of 2.21 *vs.* 5.75% with (87.5 to 96.6% of MSPE) errors due to random variations. The using of extant models for mean RpH prediction, on average, was inadequate (R^{2} < 0.50) and showed variability depending on DB sources with mean and linear biases (*P* > 0.001) for all models, except ZB8 that had no linear bias either for DB (1) or (2) (*P* = 0.343 and 0.281, respectively). Of all the extant models evaluated over DB (1), the greatest CCC were from both LES and TAM (0.58), followed by PIT and FOX, with the highest MEF (0.30 vs. 0.29), and the lowest RMSPE (5.87 vs. 5.90% of MSPE), and ALL and ZB8 with the highest CD (2.56 vs. 3.92), respectively. For DB (2) the highest CCC was from PIT and FOX (0.72 vs. 0.71), followed by ZB8 and PIT, with the highest MEF (0.51 vs. 0.44), and the lowest RMSPE (3.61vs. 3.84% of MSPE), and ALL and ZB8 with the highest CD (6.85 vs. 2.17), respectively. As a final conclusion, the new equations largely confirmed those obtained on dairy cows. The originality of our work is to provide for the first time effective coefficients that are better adapted to beef cattle production. The external validation remains to be done to confirm the effect of the integration of environmental, nutritional, and microbial factors on the RpH fluctuations, using a resilient data source, because of their vitality in accurately predicting the animal responses.

Keywords: Beef cattle, Modelling, Meta-Analysis, Prediction, pH, Rumen, Ruminal acidosis

## Résumé

Sarhan, M., 2014. *Pr é vision du pH ruminal pour bovins de boucherie: Une approche par mod é lisation physiologique. M é moire final du Master Productions Animales en R é gions Chaudes (PARC), Montpellier SupAgro, France*

Le pH ruminal (pHR) est un paramètre important du fonctionnement du rumen. La capacité de prévoir le pHR des bovins de boucherie nourris avec un régime donné sans passer par des techniques invasives pour le mesurer (*p. ex.,* canule de rumen) est important pour éviter l'acidose ruminale. Les objectifs de cette recherche étaient de : (i) identifier les variables importantes qui sont associées significativement avec pHR; (ii) rassembler les données en deux bases (BD) provenant des études de bovins réalisées *in-vivo* pour identifier les prédicteurs appropriés de pHR après avoir examiné les mesures sur les animaux et les variables alimentaires à partir d'un large éventail de régimes qui peuvent sans risque être distribués aux bovins de boucherie; (iii) évaluer des modèles de pHR existants qui soient pertinents; et (iv) développer de nouveaux modèles statistiques pour les prévisions de pHR moyens. Donc, les additifs alimentaires (*p. ex,* monensin) ont été exclus de l'analyse. Les modèles testés qui utilisent la fibre efficace (NDFp) comme une variable dépendante sont ceux de Pitt *et al*. (1996, PIT), Mertens (1997, MER), Fox *et al*. (2004, FOX), Zebeli *et al*. (2006, ZB6) et Zebeli *et al*. (2008, ZB8), et ceux qui utilisent les acides gras volatils (AGV) sont ceux de Tamminga et Van Vuuren (1988, TAM), Lescoat et Sauvant (1995, LES), *et* Allen (1997, ALL). La base de données finale a été catégorisée dans BD (1) et (2) qui comprenaient un total de 232 et 95 observations issues de 65 et 26 publications examinées par des pairs, respectivement, publiées entre 1969 et 2014. La BD contenait des informations sur les caractéristiques des animaux, la composition de la ration, la fermentation ruminale et le pH, Elles ont été utilisées pour l'évaluation indépendante et le développement de modèles de prévision de pHR moyens. Les valeurs manquantes ont été calculées en utilisant le sous-modèle de Cornell Penn Minor Dairy model (CPM-Dairy©; version 3.0, Boston *et al*. 2000) de la Cornell Net Carbohydrate and Protein System (CNCPS; version 4.0, Fox *et al*. 1992; Sniffen *et al*. 1992; O’Connor *et al*. 1993). Pour BD(1) et BD(2) respectivement, le poids vif moyen était 437±168 *vs.* 556±114 kg, la matière sèche ingérée (MSI) était de 8,57±2,62. *vs.* 9,60±2,10 kg/j, le NDFp (% MS) était de 20,3±17,0 *vs. * 17,2±14,6, et la proportion de fourrage (% MS) était 34,8±36,1 *vs.* 26,9±31,0. Les bovins utilisés étaient d'âges divers (càd, des veaux, des jeunes, des bovins adultes) représentant des systèmes de production différents (càd, finition, semi-finition, et zéro-pâturage). L’analyse intégrée de toutes les études a montré que pHR était relié positivement (*P* < 0,01) à la majorité des varibales alimentaires (càd, le fourrage, la fibre ou détergent acide [ADF], NDFp, la fibre de détergent neutre [NDF], NDF du fourrage, la lignine, les gucides, les minéraux et les concentrations ruminales d'acétate (AC) et d'ammoniac (Am) (r = 0,200-0,680 vs. 0,400-0,885) dans BD (1) et (2), respectivement. On a observé, aussi une corrélation négative (*P* < 0,01) entre pHR et la MSI, le propionate (PR), et l'amidon (corrélation de -0,330 à -0,750), et entre AGV totaux et la matière organique (MO, *P* < 0,05) dans BD (1) et (2) à l'exception des hydrates de carbone non structuraux (NFC), ainsi que de l'ingestion métabolique (% MS; *P* < 0,01) avec une corrélation entre -0,274 to -0,851. C'est pourquoi, [AGV total, (m *M*), (PR, %), butyrate (BU, %), (AC, %) et (Am, m *M*)] et les variables alimentaires (% base de MS) [MSI, Extrait éthéré, la lignine, la proportion fourragère, la NDF des fourrages, NFC, MO, le sucre, NDFp, et l'amidon ont été retenus dans le développement des modèles de prévision de pHR moyens des BD (1) et (2). Les principales différences entre les deux séries de données étaient la manière dont les pHR avaient été mesurés. Les mesures de pHR (mpHR) étaient généralement classifiées comme continues utilisent des électrodes submersible de pH ou non-continues obtenus par échantillonnage du liquide rumal, une fois ou à intervalles réguliers. Les deux mpHR ont été étudiés pour BD (1) tandis que ; seulement mpHR en continu a été inclus dans BD (2). Les équations de prévision ont été établies en utilisant l’analyse de régression de modèle mixte, avec un effet aléatoire pour l'étude et un effet fixe pour les essais. L'approche de la validation croisée (VC) a été utilisée pour évaluer les nouvelles équations de prévision. L’adéquation de modèles a été exécutée comme décrit dans Tedeschi (2006). Les critères d'information d'Akaike (AICc), le critère d'information Bayésien (BIC), coefficient de détermination du modèle (CD), coefficient de corrélation de la concordance (CCC), efficacité de la modélisation (MEF), l'erreur quadratique moyenne (RMSE), l'erreur quadratique moyenne de prédiction (MSPE), la racine de MSPE (RMSPE) et coefficient de détermination multiple (R^{2} ) ont été utilisés pour déterminer les variables du meilleur ajustement, et évaluer la prévisibilité des équations développées dans l'analyse de VC. Le biais des prévisions moyens centrés et linéaires été aussi déterminé (St-Pierre, 2003). Les 4 équations suivantes sont les meilleurs ajustements, avec les plus faibles RMSPE, le CCC et MEF les plus élevés, un CD modérée , et un % expliqué d 44 à 82 des variations du pHR sur un total de 16 nouveaux modèles développés et testé sur BD (1) et (2). L'équation (Eq.) linéaire (E): RpH = 3,32 (± 0,96) + 0,09 (± 0,004) × fourrage (% MS) + 0,02 (± 0,01) × MO (% MS) + 0,006 (± 0,003) × Am (m *M*) [AiCc = 7,81, BIC = 17.4, RMSE = 0,24, R^{2} = 0,90]; Eq. cubique (F): RpH = 5,36 (± 0,04) + 3,48 × 10-^{6} (±2,26 × 10-^{7} ) × AC^{3} (mol/100 mol) + 3,76 × 10-^{5} (±1,47 × 10-^{5} ) × Am^{3} (m *M*) [AiCc = 40,4, BIC = 48,0, RMSE = 0,32, R^{2} = 0,80]; Eq. cubique (G): RpH = 5,43 (± 0,04) + 3,37 × 10-^{6} (± 2,287 × 10-^{7} ) × AC^{3} (mol/100mol) et Eq. linéaire (H): RpH = 5,72 (± 0,018) + 0,009 (± 0,0005) × fourrage (% MS) [AiCc = 71,9, BIC = 79,3, RMSE = 0,34, R^{2} = 0,78]. L'ampleur de la performance de ces modèles après évaluation dans BD (1) et (2) respectivement, était comme suit : pour Eq. (E): CCC de 0,64 *vs.* 0,90, CD de 1,21 *vs.* 1,55, MEF de 0,37 *vs.* 0,81 et RMSPE de 2,18 *vs.* 5,34% avec 94,9 à 99,6% de MSPE des erreurs de sources aléatoires. Pour Eq. (H): CCC de 0,61 *vs.* 0,90, CD de 1,16 *vs.* 1,60, MEF de 0,37 *vs.* 0,81, et RMSPE de 2,24 *vs.* 5,56% et 98,5 *vs.* 99,4% dont était des erreurs de sources aléatoires. Pour Eq. (G): CCC de 0,64 *vs.* 0,87, CD de 1,27 *vs.* 1,79, MEF de 0,43 *vs.* 0,77, et RMSPE de 2,38 *vs.* 5,32%) avec 98,5 to 99,4% de MSPE des erreurs de sources aléatoires. Pour Eq. (E): CCC de 0,55 *vs.* 0,90, CD de 1,1 *vs.* 1,48, MEF à 0,25 *vs.* 0,82, et RMSPE de 2,21 *vs.* 5,75% avec 87,5 to 96,6% de MSPE des erreurs dues à des variations aléatoires. L'utilisation de modèles existants pour la prévision de pHR moyens, était inadéquate (R^{2} < 0.50), et en moyenne, a montré un écart selon les BD avec des biais moyens et linéaires (*P* > 0,001) pour tous les modèles, sauf ZB8 qui n'avait aucun biais linéaire aussi bien pour BD (1) que BD (2) (*P* = 0,343 et 0,281, respectivement). De tous les modèles existants évalués dans BD (1), le plus grand CCC est obtenu par les deux modèles LES et TAM (0,58), suivi par PIT et FOX, avec le MEF le plus élevé (0,30 *vs.* 0,29) et le RMSPE plus bas (5,87 *vs.* 5,90%), et ALL et ZB8 avec le CD le plus élevé (2,56 *vs.* 3,92), respectivement. Pour BD (2) le CCC le plusélevé était pour PIT et FOX (0,72 *vs. * 0,71), suivi par ZB8 et PIT, avec le MEF le plus élevé (0,51 *vs.* 0,44), et le RMSPE le plus bas (3,61 *vs.* 3,84% de MSPE), et ALL et ZB8 avec le plus CD élevé (6,85 *vs.* 2,17), respectivement. En conclusion, les nouvelles équations confirment les résultats obtenus sur les vaches laitières en précisant la réponse des bovins viande par des coefficients un peu différents. La validation externe, qui n’a pas été réalisée dans le cadre de ce travail, devra porter prioritairement sur l’effet de `l'intégration des facteurs environnementaux, nutritionnels et microbiens sur les fluctuations de pHR. Ceci à partir de données variées pour prévoir précisément la réponse des animaux.

Mots-clés: Acidose ruminale, Bovins de boucherie, Modélisation, Méta-Analyse, Prévision, pH, Rumen

## Riassunto

Sarhan, M., 2014. *Predizione di pH ruminale per bovini da carne: un approccio di modellazione fisiologico. Tesi di laurea magistrale, dipartimento di Scienze delle Produzioni Agrarie e Alimentari (DISPA) Universita' degli Studi di Catania, Facolt à di Agraria, Catania, Italy*

Il pH del liquido ruminale (pHR) è un parametro importante per controllare le funzioni del rumine. La capacità di prevedere il pHR in bovini da carne alimentati con una dieta specifica con metodologie che non prevedano tecniche invasive per le misurazioni (*p.es,* cannula di rumine) è importante per evitare l'acidosi ruminale. Gli obiettivi di questa ricerca sono stati: (i) identificare le variabili chiave che hanno un’ associazione significativo con il pHR; (ii) raccogliere i punti dei dati (BD) realizzati da studi *in-vivo* su bovini da carne per identificare i predittori adatti del pHR dopo aver considerato le misure degli animali e le variabili nutrizionali da una vasta gamma di diete; (iii) valutare i modelli esistenti per la predizione del pHR pertinenti per lo studio; e (iv) sviluppare i nuovi modelli statistici per le previsioni del pHR medio. Pertanto, gli additivi per mangimi (*p.es,* monensin) sono stati esclusi dall'analisi. I modelli testati che utilizzano la fibra fisicamente efficace (peNDF) come una variabile dipendente sono stati: Pitt *et al*. (1996, PIT), Mertens (1997, MER), Fox *et al*. (2004, FOX), Zebeli *et al*. (2006, ZB6), e Zebeli *et al*. (2008, ZB8), mentre tra quelli che utilizzano gli acidi grassi volatili (AGV): Tamminga and Van Vuuren (1988, TAM), Lescoat and Sauvant (1995, LES), e Allen (1997, ALL). Il database finale è stato classificato in BD (1) e (2) e comprendeva un totale di 232 e 95 osservazioni da 65 e 26 articoli scientifici, rispettivamente, pubblicati dal 1969 al 2014. Il BD includeva informazioni sulle caratteristiche degli animali, la composizione della razione e la fermentazione ruminale e pH, che è stato utilizzato per la valutazione indipendente e lo sviluppo di modelli di previsione del pHR. I valori mancanti non segnalati dagli autori sono stati calcolati utilizzando il sub-modello Cornell Penn Minor Dairy model (CPM-Dairy©; versione 3.0, Boston *et al*. 2000) di Cornell Net Carbohydrate and Protein System (CNCPS; versione 4.0, Fox *et al*. 1992; Sniffen *et al*. 1992; O’Connor *et al*. 1993). Il peso corporeo medio era 437±168 *vs.* 556±114 kg, assunzione di sostanza secca (ASS) era 8.57±2.62 *vs.* 9.60±2.10 kg/j, peNDF (% MS, era 20.3±17.0 *vs.* 17.2±14.6, ed il foraggio (% MS, era 34.8±36.1 *vs.* 26.9±31.0 per BD (1) e (2), rispettivamente. I bovini utilizzati erano di età diverse (vitelli, vitelloni e bovini adulti) e erano allevati secondo sistemi di produzione differenti (finissaggio, semi-finitura, pascolo- zero). L'analisi integrata di tutti gli studi ha mostrato che pHR era collegato positivamente (*P* < 0.01) alla maggior parte delle varibali alimentari (foraggio, fibra al detergente acido [ADF], peNDF, fibra al detergente neutro [NDF], NDF del foraggio, lignina, zuccheri, ceneri e le concentrazioni ruminali di acetato (AC) ed ammoniaca (Am) (r =0.200-0.680 *vs.* 0.400-0.885, in BD (1) e (2), rispettivamente. Inoltre, il pHR è risultato negativamente correlato (*P* < 0.01) con l’assunzione di sostanza secca (ASS), con il propionato (PR), con l'amido (correlazione di -0.330 to -0.750), e con la sostanza organica (MO) ed AGV totali (*P* < 0.05), in BD (1) e (2), con l’eccezione dell'ingestione metabolico (% SS) e dei carboidrati non strutturali (NFC; *P* < 0.05), con una correlazione tra -0.274 e -0.851. Di conseguenza, il contenuto ruminale di AGVt, propionato, butirrato, acetato ed ammoniaca,e le variabili alimentari (% SS, estratto etereo, lignina, la proporzione di foraggio, NDF del foraggio, NFC, MO, zuccheri, peNDF, ed amido) sono stati considerati nello sviluppo dei modelli di predizione del pHR medio dal BD (1) e (2). La differenza principale tra BD tra gli insiemi di dati consisteva nella modalità con cui il pHR è stato misurato. La misurazione del pHR (mpHR) era generalmente classificata come continua utlizzando elettrodi ad immersione, o non-continua con campionamento del fluido ruminale una volta o ad intervalli di tempo. Entrambe le tipologie di misurazione sono state considerate per BD (1) mentre; solo la modalità mpHR continua è stata inclusa in BD (2). Le equazioni di previsione sono state ottenute usando l’analisi di regressione con modello misto, con un effetto casuale per lo studio ed effetto fisso per le prove. L’approccio di validazione incrociata (VI) è stato utilizzato per valutare le equazioni di predizione. Le valutazioni dell’ adeguatezza dei modelli sono state eseguite come descritto in Tedeschi (2006). Il criterio d’informazione di Akaike (AICc), il criterio d’informazione Bayesiano (BIC), coefficiente di determinazione del modello (CD), coefficiente di correlazione delle concordanze (CCC), efficienza di modellizzaazione (MEF), l’errore quadratico medio (RMSE), l’errore quadratico medio di predizione (MSPE), la radice quadrata del MSPE (RMSPE), ed il coefficiente di determinazione multiplo (R^{2} ) sono stati utilizzati per determinare le variabili di miglior approssimazione, e per valutare la prevedibilità delle equazioni sviluppate nell’analisi de VI. Le seguenti 4 equazioni sono state scelte per il migliore adattamento dato dal più basso RMSPE, le più alte CCC e MEF e moderato CD, e hanno spiegato (0.44 - 0.82) delle variazioni esistenti nel pHR dal totale degi 16 nuovi modelli sviluppati esaminati su BD (1) e (2). L’equazione (Eq.) lineare (E): RpH = 3.32 (± 0.96) + 0.09 (± 0.004) × foraggio (% SS) + 0.02 (± 0.01) × MO (% SS) + 0.006 (± 0.003) × Am (m *M*) [AiCc = 7.81, BIC = 17.4, RMSE = 0.24, R^{2} = 0.90]; Eq. cubico (F): RpH = 5.36 (± 0.04) + 3.48 × 10-^{6} (±2.26 × 10-^{7} ) × AC^{3} (mol/100 mol) + 3.76 × 10-^{5} (±1.47 × 10-^{5} ) × Am^{3} (m *M*) [AiCc = 40.4, BIC = 48.0, RMSE = 0.32, R[2] = 0.80]; Eq. cubico (G): RpH = 5.43 (± 0.04) + 3.37 × 10-^{6} (± 2.287 × 10-^{7} ) × AC^{3} (mol/100mol) e (Eq.) lineare (H): RpH = 5.72 (± 0.018) + 0.009 (± 0.0005) × foraggio (% SS) [AiCc = 71.9, BIC = 79.3, RMSE = 0.34, R[2] = 0.78]. l’entità delle prestazioni di questi modelli dopo la valutazione su BD (1) e (2), rispettivamente, è stata la seguente. Per Eq. (F): CCC di 0.64 *vs.* 0.90, CD di 1.21 *vs.* 1.55, MEF di 0.37 *vs.* 0.81 e RMSPE di 2.18 *vs.* 5.34% con 94.9 - 99.6% di MSPE come errori di origine casuale. Per Eq. (H): CCC di 0.61 *vs.* 0.90, CD di 1.16 *vs.* 1.60, MEF di 0.37 *vs.* 0.81, e RMSPE di 2.24 *vs.* 5.56% e 98.5 *vs.* 99.4% dei quali era errore casuale. Per Eq. (G): CCC di 0.64 *vs.* 0.87, CD di 1.27 *vs.* 1.79, MEF di 0.43 *vs.* 0.77, e RMSPE di 2.38 *vs.* 5.32% di cui 98.5 a 99.4% di MSPE come errore casuale. Per Eq. (E): CCC di 0.55 *vs.* 0.90, CD di 1.1 *vs.* 1.48, MEF di 0.25 *vs.* 0.82, e RMSPE di 2.21 *vs.* 5.75% con 87.5 a 96.6% di MSPE a causa di variazioni casuali. L’utilizzo di modelli esistenti per la predizione di pHR, mediamente, è stata inadeguata (R^{2} < 0.50) e ha mostrato variabilità a seconda delle fonti di BD con bias medi e lineari (*P* > 0.001) per tutti i modelli, ad eccezione di ZB8 che non presentava bias lineare sia per BD (1) o (2) (*P* = 0.343 and 0.281, rispettivamente). Di tutti i modelli esistenti valutati su BD (1), il CCC è risultato maggiore per LES e TAM (0.58), seguito da PIT e FOX, con il più alto MEF (0.30 *vs.* 0.29), e il più basso RMSPE (5.87 *vs.* 5.90% di MSPE), e ALL e ZB8 con il più alto CD (2.56 *vs.* 3.92), rispettivamente. Per BD (2) il più alto CCC è risultato associato a PIT e FOX (0.72 *vs*. 0.71), seguiti da ZB8 e PIT, con il più alto MEF (0.51 *vs.* 0.44), e il più basso RMSPE (3.61 *vs.* 3.84% di MSPE), e ALL e ZB8 con il più alto CD (6.85 *vs*. 2.17), rispettivamente. Come conclusione finale, le nuove equazioni in gran parte confermano quanto già ottenuto su vacche da latte. L’originalità del nostro lavoro è quello di fornire per la prima volta i coeefficenti che meglio si adattano alla produzione di carne bovina. La convalida esterna rimane da fare per confermare l'effetto dell'integrazione di fattori ambientali, nutrizionali e microbici sulle fluttuazioni di pHR, utilizzando dati resilienti in grado di predire con precisione le risposte degli animali.

Parole chiave: Acidosi ruminale, Bovini da carne, Modellazione, Meta-analisi, Previsione, pH, Rumen

## Abbreviations and acronyms

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## 1. Introduction

pH is a measure of the decimal logarithm of the reciprocal of hydrogen ion, *a* H+, concentration in a solution (Sørensen, 1909). Ruminal fluid pH (RpH) is a measure of the acidity or the alkalinity of the ruminal contents, and an important determinant of rumen functionning (Bannink, 2007). The ability to predict the RpH of beef cattle fed a given diet is important to estimate effects on ruminal digestion of fiber (Fox *et al*., 2000), microbial protein synthesis (Russell *et al*., 1992), and to avoid ruminal acidosis (RA, Schwartzkopf-Genswein *et al*., 2004). RA is recognized as a continuum of degrees of ruminal acidity (Britton and Stock, 1987) and it is characterized by the uncompensated drop in RpH (Krause and Oetzel, 2006). RA is categorized as acute ruminal acidosis (ACRA) or sub-acute ruminal acidosis (SARA), that share a similar aetiology (Owens *et al*., 1998) but are considered very different clinical diseases (Appendix, App; Table 1). SARA occurs when the production of volatile fatty acids (VFAs) in the rumen exceeds the ability of the gut or tract to remove or neutralize acids produced (Allen, 1997) with RpH depression between 5.00 to 5.50 (Garrett *et al*., 1999). ACRA is an overt illness caused by consumption of an excessive quantity of readily fermentable carbohydrate (*i.e.* starch) resulting in RpH falling below 5.2 (Krehbiel, 2014). Therefore, RpH could represent a vital homeostatic parameter (Sauvant, 1994) to the complex ruminal mechanisms triggering the incidence of SARA, as well as other important indices e.g., lactic acid concentration (App. Table 2).

The reliable and accurate diagnostic test for RA is obtained through RpH measurements (RpHms). The techniques for RpHms is principally divided into 1) oro-ruminal probes (Geishauser, 1993), rume- nocentesis (Nordlund *et al*., 1994, 1995), direct sampling via oral stomach tube (Nocek, 1997), and ruminal cannula (Duffield *et al*., 2004) 2) continuous indwelling electrodes (Bevans *et al*., 2005) 3) Stand-alone systems (Penner *et al*., 2006). These tests (*i.e., points 1, 2, and* 3) have been used to collect ruminal fluid samples for RpHms under both experimental and field conditions (Garrett *et al*., 1999; Duffield *et al*., 2004; Shen *et al*., 2012). However, most of these RpHms methods have both advantages (*i.e. point* 3) measure the occurrence of RA in unrestrained cattle, and inherent limitations (*i.e. point* 1) linked to susceptibility to salivary contamination resulting in higher RpH values than samples collected from rumen cannula. RpHms, also, tended to be more invasive (*i.e. point* 1), and restrict animal mobili- ty (*i.e. point* 2) leading into inaccurate estimations of the real RpH (Li *et al.*, 2009; Shen *et al*., 2012).

The regulation of RpH is a complex process that influences the ruminal health and functionality. This involves aspects affecting ruminal VFAs production (e.g. rate of fermentation, meal size and frequency, acid removal from the rumen, and fermentation pathway; Li *et al*., 2013; Penner, 2014). Also, the VFAs metabolism (Bergman, 1990), and VFAs absorption (Aschenbach *et al*., 2010) greatly influenced the mean RpH. Several other factors correlate with the mean RpH and influence the rumen acid-base mechanisms (e.g. rumination and saliva production; Bannink and Tamminga, 2005). Furthermore, the composition of the diet, such as the effective fiber (Mertens, 1997), the feed intake (e.g. forage intake; Adams and Kartchner, 1984), and digestibility (e.g. starch digestibility; Nozière *et al*., 2010, 2011) have been shown to be effective on the mean RpH. Additionally, feed additives (e.g. ionophores, monensin, and bacteriocins; Russell and Baldwin, 1979), and feeding management strategies, which help in reducing the feed intake variations to reduce the risk of SARA, increased RpH (Schwartzkopf-Genswein *et al*., 2003). Consequently, the ruminal fermentation characteristics, the digestion rate (Pitt and Pell, 1997), and the time when mean RpH is < 6.0 (Lechartier and Peyraud, 2010) have been suggested to be useful to control RpH. Therefore, RpH might be a good candidate for modelling the change in animal responses to diets (Bannink, 2007). However, the predictability of RpH is still poor (Kolver and De Veth, 2002; Dijkstra *et al.,* 2012; Mills *et al.,* 2014).

Few attempts have been made to model the mean RpH and most models used a rather empirical approach for its prediction (Baldwin *et al*., 1987a, b; Argyle and Baldwin, 1988, BAL; Tamminga and Van Vuuren, 1988, TAM; Lescoat and Sauvant, 1995, LES; Pitt *et al*., 1996, PIT; Mertens, 1997, MER; Allen, 1997, ALL; Fox *et al*., 2004, FOX; Zebeli *et al*., 2006, ZB6; and Zebeli *et al*., 2008, ZB8). Several of these modelling approaches have been presented to either relate molar proportions of the total concentrations of ruminal VFAs formed (tVFAs) (*i.e.,* TAM, LES, ALL) to predict the mean RpH. Others represent general nutritional factors, such as the dietary content of the physically effective NDF (peNDF) (*i.e.,* PIT, MER, FOX, ZB6 and ZB8) to the mean RpH. Despite the fact that RpH is also affected by other factors such as, meal frequency (Zhang, *et al*., 2013a, b) and ruminal ammonia concentrations (NH4) (Aschenbach *et al*., 2011; Lu *et al*., 2014) were not included. Nevertheless nu- merous other factors (App. Table 3) that strongly dictate the ruminal compartment and fermentation and hence could help determine RpH are still not considered by the current prediction models (Table 1).

Earlier BAL models, introduced the effect of RpH on tVFAs yield based on *in vitro* results. Later, TAM model investigated feed intake effect on the rate of VFAs clearance and production, reflecting how they are correlated with, and dependent on, the mean RpH, based on *in vivo* results. Similarly, LES developed a mechanistic model by the Institut National de la Recherche Agronomique (INRA) from which the mean RpH was predicted empirically from the tVFAs concentrations. Further, ALL adopted the same methodology for RpH prediction. Conversely, PIT model predicted the tVFAs and the mean RpH based on inputs, assumptions, and equations published in the Cornell Net Carbohydrate and Pro- tein System (CNCPS) model (Fox *et al*., 1992; Sniffen *et al*., 1992; O’Connor *et al*., 1993). The PIT model predicted the mean RpH based on BAL concept of the balance between buffering of ruminal liquid and acid production rate, and was considered to be the first to relate the peNDF proportions to RpH. Likewise, MER, FOX, ZB6, and ZB8 predicted the mean RpH based on “the peNDF concept”.

Unfortunately, the majority of these efforts (*i.e.,* ALL, MER, TAM, ZB6 and ZB8) that contributed to modelling RpH used data sources, mainly, from dairy cows (n = 244, 114, 99, 131 and 187, respec- tively) for its development, with only LES and PIT considering limited data from beef cattle (n = 57 and 10, respectively) and also sheep (PIT; n = 1). Athough FOX considered data similar to PIT, the number of observations used was not reported. The main limitation of these models (e.g., ALL, TAM), however, lies in their methodological construction that used simple regression analysis, without ac- counting for random experimental effects, and thus, absolute values may be estimated with considera- ble biases (St-Pierre, 2001, 2003). In addition, variations in the RpHms techniques from which these models were developed in the first place may provide additional errors due to different experimental conditions. Until now, the performance of these models when applied against an independent dataset for beef cattle is not available yet, so RpH prediction remains a big challenge (Mills *et al.,* 2014).

The purposes of the present study were, therefore, to: (1) attempt determining the factors that ap- pear to have a significant relationship with the animal responses to the mean RpH; (2) identify suitable predictors of the mean RpH from rumen fermentation characteristics, dietary compositions *i.e.,* neutral detergent fibers (NDF) and starch, and dietary intake *i.e.,* dry matter intake (DMI); (3) develop statisti- cal models to predict the mean RpH based on *in-vivo* beef cattle measurements; (4) evaluate, compare, and challenge the existing published RpH prediction models (*i.e., * ALL, CNCPS, INRA, and ZB8) against the observed data for an independent appraisal of their performance in predicting the mean RpH using beef cattle that have been fed diets from different sources covering a wide range of possibilities.

### 1.1 Changes in the Mean Ruminal pH Profile of Beef Cattle during Acidosis

Transition from feeding high-quality pastures to grain-based diets in beef cattle can lead to ACRA and SARA. These incidence may result in a complex intra-ruminal processes (Figure 1; adapted from Schwartzkopf-Genswein *et al*., 2003). As noted by Nagaraja and Titgemeyer, (2007) for feedlot cattle, the average RpH typically around 5.80 to 6.20 during the feeding cycle. A drop in the RpH below 5.80 (Beauchemin *et al*., 2001; Moya *et al*., 2011), 5.60 (Owens *et al*., 1998; Cooper *et al*., 1999; Brown *et al*., 2000; Bevans *et al*., 2005), or 5.50 (Wierenga *et al*., 2010; Zhang *et al*., 2013a) have been used to signify SARA. Most researchers use a drop in RpH below 5.0 (Nocek, 1997), or below 5.20 (Wierenga *et al*., 2010) as an indication for ACRA. Others have suggested that the ACRA is identified by an increase in ruminal lactate higher than 5 m *M* (Aschenbach *et al*., 2010) or higher than 50 m *M* (Goad *et al*., 1998; Nagaraja and Titgemeyer, 2007). The lowest mean RpH (nadir) in the feedlot cattle usually varies from 5.0 to 6.50 (Beauchemin *et al*., 2001; Koenig *et al*., 2003).

When RpH is maintained above 5.50, equilibrium exists between producers and utilizers of lactic acids (Nocek *et al*., 1997). In contrast when RpH is less than 5.50, S.bovis multiplies until RpH is less than 4.70, a pH that allows an increase in acid-tolerant Lactobacillus growth (Allison *et al*., 1978). Both of these bacterial species produce D and L-lactic acid, which is metabolized more rapidly than D-lactate, the RA is due in large part to the accumulation of the latter (Slyter, 1976; Bolton and Pass 1988; Nagaraja and Titgemeyer, 2007; Mills *et al.,* 2014).

illustration not visible in this excerpt

Figure 1.Metabolic consequences of feed intake in finishing feedlot cattle

### 1.2 Mathematical Modelling in Animal Nutrition

Traditionally, quantitative research into ruminal functions pathways (e.g. metabolism, digestion, etc.) has been empirically centred on statistical analysis of experimental data. Recently, more attention has been given to improve the understanding of the underlying mechanisms that govern those processes through mathematical modelling (Dijkstra, 1993). A cattle nutrition model is defined as an integrated set of equations and transfer coefficients that describe their various physiological functions (Gill *et al*., 1989). Normally, the statistical models tend to be well suited to practical application for rapid diet evaluation or larger-scale inventory purposes (Odongo *et al*., 2008). Modelling efforts to predict the physiological response of the animal to a dietary change from the thirty’s until now have been well- documented. Models could be classically categorized into empirical and mechanistic models (Kebreab *et al*., 2009). Empirical models (EM) provide a best fit to data obtained at the production level (Dijkstra *et al*., 2012) that describe empirical relationships to predict a single aspect of nutrition, such as methane emissions (Kriss, 1930), and microbial synthesis in the rumen (Oldick *et al*., 1999). On the other hand, mechanistic models incorporate concepts about the underlying biology from lower level of aggregation (Dijkstra *et al.*, 2005). These models attempt to be more dynamic in their construction, such as the mechanistic model for beef steers growth of Oltjen *et al*. (1986). More specifically, these models play a useful role in the evaluation of hypotheses and in identification of areas where knowledge is lacking as demonstrated in many reviews (e.g., Dijkstra *et al*., 2002; Bannink and Tamminga, 2005; Kebreab *et al*., 2009). But it must be underlined that as such, models serve a specific goal for which they were derived (France.and.Kebreab, 2008). However, the use of models to assist in production decisions, is limited by information ‘model inputs’ typically available on the farm conditions (Tedeschi *et al*., 2005). To that end, EM seems to be a robust tool valuable to improve the efficiency of animal feeding system.

#### 1.2.1 Prediction of the Mean Ruminal pH from Dietary Compositions

##### 1.2.1.1 Mertens, (1986-1997)

There are several ways of characterizing diet physical fiber and over the years various terms have been introduced. Effective fiber, or the effective NDF (eNDF), is the term originally proposed for dairy rations in the US by Mertens (1986) for representing the ability of a feed to replace forage in a ration so that milk fat percentage is maintained. Thus, the eNDF value of a feed depends upon its particle length, buffering capacity, fermentation rate, and other inherent characteristics (Allen, 1997). In practice the eNDF content of a feed is determined by measuring its NDF content, then measuring the percent of the NDF remaining on a 1.18 mm screen after vertical shaking of the dry feed (Mertens, 1986). The values are then adjusted for density, hydration, degree of lignification of the NDF, and other factors based on judgment of the user (Mertens, 1986). It seems that the difficulty with the eNDF concept is the lack of a standardized method of assessment, and thus assignment of eNDF values to feeds is somewhat arbitrary (Beauchemin *et al*., 2003, 2005). Furthermore, milk fat synthesis is affected by numerous factors other than dietary fiber (Bauman *et al*., 2006), and obviously is not relevant for beef cattle.

The term physically effective fiber (peNDF) was introduced by Mertens, (1997; MER) to refine the concept of effective fiber. Physically effective fiber relates solely to the particle size of feed and is an indication of its potential to stimulate chewing (Allen, 1997; Yang *et al*., 2001). Thus, peNDF differs from eNDF in that peNDF is narrowly defined in terms of chewing, whereas eNDF encompasses more factors (Beauchemin and Yang, 2005). The physical effectiveness factor (pef) of a feed ranges from 0 to 1.0; pef is multiplied by NDF content to determine peNDF content of the feed (Mertens, 1985a, b). Long grass hay with a theoretical NDF content of 100% is used as a reference feed and has a pef of 1.0 and a peNDF content of 100% (Mertens, 1997). The pef of other feeds are relative to this standard. A limitation to using chewing time to indicate the physical effectiveness of feeds is the need to rely on book values for pef (NRC, 1984, 1996, 2000). Thus, sieving methods that measure particle length of feeds are used to determine pef, based on the concept that long particles retained on sieves represent particles that require chewing (Allen, 1997; Yang *et al*., 2001; Beauchemin and Yang, 2005).

The original concepts of eNDF and peNDF were based on measuring particle length using an oscil- lating dry-sieving technique (Mertens, 1997). However, due to the ease of use, the Penn State Particle Separator with three sieves (openings of 19.0, 8.0, 1.18 mm; original version has only 19.0 and 8.0 mm sieves) and a bottom pan has over the years been widely adopted on-farm, to measure particle length of feeds (Lammers *et al*., 1996; Kononoff *et al*., 2003). The pef of a feed or diet is the total proportion of material retained on either the top two (pef>8), or all the three sieves (pef>1.18; Mertens, 1980). The ad- vantage of using three sieves is the values are more closely in line with the previous eNDF values (Mertens, 1983). The disadvantage is that the pef>1.18 values for forages with differing chop lengths are not well differentiated (Oba and Allen, 1999; Beauchemin *et al*., 2006). Furthermore, whole and rolled grains and pelleted supplements are trapped on the 1.18-mm sieve, thereby inflating the pef>1.18 values of the total mixed rations (TMR) (Beauchemin *et al*., 2006). This limitation can be overcome by calcu- lating dietary peNDF solely from individual forages, omitting pelleted feeds (Varga *et al*., 1998; Mertens, 2000; Beauchemin *et al*., 2006). Still, peNDF assessment is confounded by this technique.

There is sometimes confusion between the terms eNDF and peNDF, and often they are incorrectly used interchangeably (Beauchemin *et al*., 2006). While peNDF and eNDF are highly correlated, eNDF can be greater than peNDF for feeds that promote greater milk fat percentage, but do not stimulate chewing activity (Mertens, 1997). Such would be the case for certain fat supplements and feeds con- taining intrinsic buffering capacity (Leventini *et al*., 1990; Kohn and Dunlap, 1998). Conversely, eNDF can be less than peNDF for feeds that lower milk fat content without affecting chewing time (Mertens, 2000). Such may be the case for certain feeds containing sugars (Golombeski *et al*., 2006). Because of these evidence mentioned above, MER compiled a database containing 114 observations from 26 cita- tions to determine the effective fiber requirement for RpH as a better indication of ruminal health than the maintenance of milk fat (Table 1). The main conclusions from this work, as stated by MER, were the need for further research to (1) identify whether differences in concentrate source, supplemental buffers, forages sources, feeding frequency, and type of ration (total mixed versus separate feeding) affect the requirements for peNDFand eNDF; and (2) verify whether these requirements for animal longevity is different from the requirements to maintain a stable RpH through identifying of the feeds characteristics that influence their effectiveness in maintaining optimal ruminal function.

##### 1.2.1.2 Cornell Net Carbohydrate Protein System, (1992-2008)

In ruminants, the prediction of animal performance from dietary ingredients has been confounded by the impact of ruminal fermentation on host nutrition and difficulties in predicting its effect on the rumen functions (Russell and Strobel, 2005). The Cornell Net Carbohydrate Protein System (CNCPS; Fox *et al*., 1995; Russell *et al*., 1992; Sniffen *et al*., 1992) continues to be the most widely used predic- tion model of those aspects (Dijkstra *et al*., 2005). Pitt *et al*. (1996; PIT), contributed to the improve- ment of the CNCPS by adding a series of equations to predict the mean RpH. Firstly, PIT attempted to relate the RpH and dietary measures from 14 published studies with lactating dairy cows, steers, and, in one case, sheep into an empirical sub-model for RpH predictions. Indeed, PIT succeeded in relating the RpH and total effective NDF (eNDF) in an empirical relationship. PIT considered the effective fiber as the percentage of NDF in each feed, depending on its physical processing, that contributes to meeting NDF requirements (Mertens, 1992). However, none of the variation in RpH from PIT equation was explained for eNDF greater than 50% (Table 1), but as eNDF decreased, RpH decreased.

Secondly, PIT attempted to describe the relationship between eNDF in a more mechanistic fashion, based on the equilibrium between ruminal buffering (RB), and its acidity (Ra). In other words, PIT calculated the buffering of ruminal liquid through a range of RpH; the RpH at which RB and Ra are equal is taken as the equilibrium for the RpH. Dijkstra *et al*. (1992) developed an empirical model to predict the salivary flow in dairy cows from DMI and diet NDF and two contributions to RB were rec- ognized as saliva and rumen-resident NDF. In order to incorporate the effect of particle size on rumina- tion; PIT re-defined the Dijkstra *et al.* (1992) concept by converting NDF values into eNDF, and saliva production then was a function of DMI and eNDF. Eventually, three facets of PIT work were incorpo- rated into later versions of CNCPS models (version 5 and 6; Fox *et al*., 2000, 2004; Tylutki *et al*., 2008, respectively) to predict the mean RpH and efficiency of microbial growth in ruminants. Briefly, PIT described the relationship between peNDF, RpH and the fermentable carbohydrate (FC) digestion. First, RpH was a function of eNDF which was defined by cell wall content and particle size. Secondly, yields of the non-fibre carbohydrate (NFC) bacteria were decreased as a function of eNDF. Thirdly, as RpH declined, maintenance energy of FC bacteria was increased and rate of fibre digestion was de- creased.

Similarly, Fox *et al*. (2004; FOX) adopted ‘the peNDF concept’ to predict RpH for dairy cattle; as the effectiveness of the NDF in stimulating saliva flow, and ruminal fluid dilution rate (RFDR) is man- ifested in its ability to stimulate chewing, rumination and rumen motility. FOX considered the peNDF as the percentage of NDF that is retained on a 1.18 mm screen as described by Allen (1997), and pro- vided its values in CNCPS feed library (version 4; Fox *et al*., 2003). The integration of these principles are supported by the findings of Davis *et al*. (1964) and Allen, (1997) that dairy cows fed grain-based diets produced less saliva than those fed forage and had a slower RFDR, respectively. FOX has argued that when cattle are fed diets deficient in fiber and rich in grain, RpH can decline significantly. If the RFDR is rapid, VFAs can pass out of the rumen, and be absorbed from the abomasum, where the pH is lower and passive diffusion is more rapid (Russell, 2002). Once more, FOX equations were integrated into the animal growth sub-model in CNCPS. Furthermore, Tylutki *et al*. (2008) re-designed and up- dated the final version of CNCPS without modifying FOX. Therefore, CNCPS model uses NDF con- tent of the ration and physical properties of NDF to predict mean RpH for all ruminants.

##### 1.2.1.3 Zebeliet al. (2006) and (2008) models

In Germany, using a meta-analysis, Zebeli *et al.* (2006; ZB6) generated a data file containing 131 treatment means from 33 dairy cattle experiments to predict the mean RpH from the dietary peNDF proportions (Table 1). Zebeli *et al.* (2006) showed that an increase in the peNDF up to 30% (as a percent of the dry matter (DM) increased the mean RpH to a plateau of 6.20, after which no further increase was significantly achieved. The peNDF was measured as the proportion of particles retained on the 8-mm screen (peNDF>1.18), and the mean RpH responded quadratically to those proportions. As such, the increasing of the dietary peNDF increased the mean RpH. Similarly, implementing the same modeling approach, Zebeli *et al*. (2008; ZB8) used 187 treatment means from 45 dairy cows studies to predict the mean RpH from the dietary peNDF proportions (Table 1). Zebeli *et al*. (2008) confirmed that an increase in the peNDF up to 31.2% (DM basis) increased the mean RpH to a plateau value of 6.27, after which no further increase was achieved. Further, the required peNDF increased quadratically with increases in concentration of rumen degradable starch from grains and with increases of DMI.

#### 1.2.2 Prediction of the Mean Ruminal pH from Ruminal Fermentation end-products

##### 1.2.2.1 Tamminga and Van Vuuren, (1988)

In the Netherlands, Tamminga and Van Vuuren, (1988; TAM) reviewed the biological principles of formation and utilization of end-products of lignocellulose degradation in ruminants. However, earlier (Baldwin *et al*., 1987a,b; Argyle and Baldwin, 1988; BAL) efforts attempted to represent the effects of particle dynamics on rumen functions. Accordingly, large amounts of starch, and soluble carbohydrates, as well as long periods of low RpH substantially reduced the ruminal fibrolytic activity. TAM stressed on the non-energy-yielding nutrients, such as, organic compounds (OC) and their importance to support animal energy. Therefore, TAM distinguished OC on the basis of the type(s) of precursors they can yield. Hence, OC could be divided into nutrients which can be used as precursors for the synthesis of lipids (ketogenic), proteins (aminogenic) and lactose (glycogenic). TAM recognized acetate (AC) and butyrate (BU) as ketogenic, and propionate (PR) as glycogenic, with a ratio, in which tVFA are formed and supplied to the host animal, of 65:20:15 for AC: PR: BU, respectively.

However, TAM argued that substantial deviations from this ratio are possible as a result of the rate of VFAs degradation and RpH. In addition, the greater absorption rate of acids with longer chain length proceeds more easily through diffusion, at low RpH levels or at higher VFAs concentrations (Stevens, 1970). Moreover, such deviations are the result of large quantities of easily degradable carbohydrates (Ørskov, 1977) or at high levels of feed intake (Sutton, 1986). Despite, TAM work could be considered as a description of the types of nutrients that are mainly used to supply animal energy; the Tamminga and Van Vuuren (1988) analysis culminates in an empirical model describing the relationship between RpH and tVFAs production. TAM developed this model from a dataset of 244 treatment means pooled from dairy cows studies, and resulted in 71% explanation of the variations in the mean RpH (Table 1).

##### 1.2.2.2 Institut National de la Recherche Agronomique, (1995)

In France, Lescoat and Sauvant (1995; LES) developed a mechanistic model which determined the mean RpH empirically from the ruminal fermentation characteristics. LES adopted the end-products of ruminal fermentation (*i.e.,* VFAs) that arise from the fermentation of carbohydrates and amino acids. As previously mentioned in the earlier (Baldwin *et al*., 1987a,b; Argyle and Baldwin, 1988; BAL) and Dijkstra *et al*. (1992) models, LES defined four categories of VFAs: AC, PR, BU, plus the branched- chain VFAs. However, BAL and Dijkstra *et al*. (1992) used the stoichiometric relationships developed by Murphy *et al*. (1982) which recently has been proved to introduce inaccurate and biased prediction (Bannink *et al.* 1997; 2006). Obviously, the empirical RpH predictions using the tVFAs concentration are moderately accurate when ruminal VFAs is accurately determined either by direct measurements (Bannink *et al*., 2006a, 2008) or estimated through a stoichiometric approach (Morvay *et al*., 2011). Nonetheless, there is a strong body of evidence showing that the tVFAs yields from rapidly fermentable carbohydrates is dependent on the RpH itself (Bannink *et al*., 2011; Dijkstra *et al*., 2012). Fortunately, in the analysis of Lescoat and Sauvant (1995) they have used an empirical approach for ruminal VFAs assuming the importance of degradable cell-wall carbohydrates from *in sacco* measurements at INRA.

Murphy *et al*. (MUR; 1982) were among the first to derive the VFAs stoichiometry from *in vivo * data derived from sheep, cattle, steers and buffalos. Several models of rumen function have been published since to account for the effect of RpH based on MUR concept. Subsequently, the dynamic mechanistic models of BAL and Dijkstra *et al*. (1992) introduced the impact of the ruminal acidity (Ra) on the cell wall carbohydrates degradation (Baldwin *et al*., 1987a,b) and on the type of VFAs produced (Argyle and Baldwin, 1988; Bannink *et al*., 2008). Several other attempts have been made since to derive new coefficients either by incorporating nutritional factors of grass-silage from sheep (Friggens *et al*., 1998) or microbial factors exclusively from dairy cows (Bannink *et al*., 2000; Nagorcka *et al*., 2000), as well as applying thermodynamic laws (Kohn and Boston, 2000). More efforts, subsequently aimed for simulating the ruminal VFAs fermentation and its effect on RpH have been introduced by Bannink, (2006); Sveinbjörnsson *et al*. (2006) and Nozière *et al*. (2010). Recently, Alemu *et al*. (2011) demonstrated that these efforts explained less than 23% of the tVFAs variations and individual molar proportions produced, thus, their reliability for RpH predictions may be questionable. The reasons for this low performance could be due to the different levels of aggregation chosen in these studies (Bannink and Tamminga, 2005) as they were all based on the VFAs concentrations rather than the production rates (Nozière *et al*., 2011). In addition, despite their complexity, the concepts from which they were mainly based are not commonly available in the literature (*i.e.,* Kohn and Boston, 2000). Specifically, it is beyond the scope of the present study to test these models. However, in any case, one can speculate that for mean RpH prediction in beef cattle it would to be inadapted. This is because of the unsatisfactory results of VFAs predictions (Morvay *et al*., 2011), and data sources used (mainly from dairy cows) in their development which considered as vital factors for accurate RpH prediction.

Luckily, LES at that time used a new method to obtain more realistic values of the molar proportions of the tVFAs. For this purpose, LES assembled a database of literature results from beef cattle contains 130 results from 45 experiments, in which the main parameter was the percentage of concentrate and the measured tVFAs. Consequently, LES analysis resulted in quadratic equations describing the tVFAs evolution. From the above results, using intra-experiment linear regression; LES predicted mean RpH empirically using ruminal tVFAs from a total of 57 treatments means (Table 1).

##### 1.2.2.3 Allen, (1997)

In the US, similarly to LES and TAM, Allen (1997; ALL), ALL predicted mean RpH from the tVFAs concentrations. However, ALL used an empirical approach from 99 treatment means resulting from 25 dairy cattle experiments (Table 1). ALL found that VFAs were (*P* < 0.001) weakly negatively related to mean RpH. This was likely related to large variation between diets in removal, RB and neutralization of acids in the rumen that subsequently, affected this relationship. Furthermore, ALL investigated ‘the peNDF concept’ in his analysis and stressed on its limitation, which mainly lies in not taking into consideration the differences in ruminal fermentability of the non-fiber substrate. Hence, peNDF effect is due to chewing and ruminating activities, meal size, rumen motility and shifts in the site of grain digestion (Allen, 1997). Therefore, as noted previously, because peNDF and eNDF are indications of chewing time, and mastication increases salivation, these terms are indirectly related to the mean RpH. Obviously, ALL pointed out that a high degree of variability in the mean RpH prediction from peNDF remains, and is caused by many other uncontrolled variables (*i.e.,* starch level).

ALL showed that differences in the percentage of organic matter truly digested in the rumen (OMTD) between diets might be the most important single factor affecting the mean RpH. ALL also noted that adaptive changes in rumen papillae length to increase surface area, due to diets varying in rumen digestible OM, might be an important factor affecting the susceptibility of animals to suffer from RA. The fraction of OMTD varies greatly among diets and affects the fiber requirement for dairy cattle (Allen, 1997). Subsequently, this variation affects the amount of fermentation acids produced and directly affects the amount of peNDF that is required to maintain adequate RpH (Allen, 1997). Also, the fraction of acids absorbed post ruminally increased as the liquid passage rate (Pr) increases and as RpH increases (Allen, 1997). ALL indicated that direct buffering effect from feeds alone comprises a small portion of RB capacity resulting from saliva flow and that inherent buffering of roughages in

Table 1. Published equations used to predict the mean ruminal pH for ruminants

illustration not visible in this excerpt

typical dairy diets high in NDF is small. The bicarbonate (HCO3-), RFDR, and phosphate buffers in saliva neutralize acids produced by fermentation of OMTD. Further, balancing the production of fermentation acid and buffer secretion is a major determinant of mean RpH (Allen, 1997). Allen, (1997) concluded that EM give reasonably accurate predictions, and accuracy may be improved further by including % of forage NDF or measurements of peNDF combined with estimates of OMTD.

## 2. Materials and Methods

### 2.1 Database Compilation

Treatment mean data were collected from 65 peer-reviewed papers spanning from 1969 to 2014, resulting in a total of 273 ruminal pH (RpH) observations for beef cattle. A search was conducted for articles published until 2014 with search terms: rumen pH and beef for inclusion in a meta-analysis approach (Sauvant *et al*., 2008). A description of the animal characteristics, diet composition, and ru- minal fermentation variables forming the data sources collected from different publications for the crea- tion of 1st dataset DB (1), and 2nd dataset DB (2) are summarized in (App. Tables 4 and 5, respectively). A summary of the publications used in DB (1) and (2) is presented in (Tables 6 and 7, respectively) and a comprehensive description of studies is provided in the (App. Tables 8, 9, 10, 11, 12, 13, and 14).

Only data from *in-vivo* beef cattle studies were included. Treatments designed to specifically eval- uate feed additives (*e.g.*, monensin, tannins, enzymes, fumaric acid) were excluded (n = 41 removed) from the final data sets (App. Table 11), although some of the control diets included ionophores. It is noteworthy that all the data points used were evaluated for outlier’s detection and none were identified. Cattle used were of various ages (calves, yearlings, mature) and represented various production systems (backgrounding, finishing, transition, zero-grazing, all-forage diets, and so forth; App. Table 9). Initial body weight ranged from 85 to 742 kg and from 260 to 680 kg for DB (1) and (2) (App. Tables 6 and 7, respectively). Animals were of different breeds (Angus, Aberdeen, Angus-Hereford, British, Crossbred, Charolaise, Friesian, Holstein, Hereford, and Simmental) and their crosses. Dairy breeds (*i.e.,* Holstein, Jersey) that were raised for meat in the reported studies, were included in the final databases.

The selection of a study for its inclusion in the database was based on several criteria. Firstly, RpH values needed to be reported in the paper and adequate description of the diets (ingredient and chemical composition; App. Table 12) was needed. Only studies reporting DMI (or where DMI could be calcu- lated) were included. Information on rumen fermentation end-products including tVFAs concentrations, molar proportions of individual VFAs (acetate, AC; propionate, PR; butyrate, BU), and ammonia con- centration (Am) were recorded when reported. The data sets included studies that investigated the ef- fects of feeding level, proportion of concentrate, supplementation, forage type (grasses, legumes, whole crops), maturity of forage crops at harvest, and silage fermentation. Hence, a wide range of dietary compositions was represented from different continents (*i.e.,* Americas, Asia, and Europe).

### 2.2 Database Description

The majority of the studies were from North America (App. Table 9). Studies were conducted in Canada with feedlot finishing diets composed of 88 to 90% (DM basis) barley grain (dry-rolled and ground) (Krause *et al*., 1998; Pylot *et al*., 2000; Beauchemin *et al*., 2001; Ghorbani *et al*., 2002; Beauchemin *et al*., 2003; Koenig *et al*., 2003; McGinn *et al*., 2004; Soita *et al*., 2003; Schwartzkopf- Genswein *et al*., 2004; Beauchemin and McGinn, 2005; Bevans *et al*., 2005; Beauchemin and McGinn, 2006; Paton *et al*., 2006; Beliveau and McKinnon, 2009; Wierenga *et al*., 2010; Yang *et al*., 2010a, 2010b; Kerckhove *et al*., 2011; Walter *et al*., 2012; Hünerberg *et al*., 2013b; Friedt *et al*., 2013; Koenig and Beauchemin, 2013; Li *et al*., 2013; Schwaiger *et al*., 2013; Yang *et al*., 2013; Vyas *et al*., 2014a) or barley grain supplemented with dried distillers grains plus solubles from corn or wheat (DDGS) (Li *et al*., 2011; Moya *et al*., 2011; Walter *et al*., 2012; Hünerberg *et al*., 2013a, 2013b). Other Canadian stud- ies with feedlot cattle used high grain diets based on high-moisture ear corn (76% DM; Fellner *et al*., 2001), wheat (30 to 89% DM; He *et al*., 2014), or dry rolled corn (56.2% DM) and corn DDGS (27.6% DM; Narvaez *et al*., 2014). The forage-based diets contained a variety of forages, including mixed spe- cies grasses, alfalfa and sainfoin freshly cut or as hay at different maturity stages (Chung *et al*., 2013). Other studies fed barley silage (55% DM, Hünerberg *et al*., 2013a; 70% DM, Vyas *et al*., 2013) or a mixture of barley silage and chopped grass hay (40% and 10% DM, respectively; Vyas *et al*., 2014b).

In most of the studies conducted in the US, feedlot cattle were fed high grain corn-based diets, with grain accounting for 60 to 90% of DM processed using various methods (cracked, dry-rolled, steam- flaked, high moisture, whole shelled, and ground; Rumsey *et al*., 1970; Oltjen *et al*., 1971; Lee *et al*., 1982; Zinn, 1990; Freeman *et al*., 1992; Murphy *et al*., 1994; Barajas *et al*., 1998; Cooper *et al*., 1999; Erickson *et al*., 2003). In the study of White *et al*. (1969) steers were fed a total mixed ration (TMR) comprising of 70% DM sorghum grain, 20% DM alfalfa hay and either 10% DM rice straw or rice hulls. In the study by Leventini *et al*. (1990), cattle were fed a diet with 50:50 (DM) grass hay: barley grain. Others used a blend of steam-flaked barley and corn (Zinn and Barajas, 1997) accounting for 76% of dietary DM. The forage-based diets used tall grass-prairie hay (90% DM, Köster *et al*., 1996; 95% DM, Olson *et al*., 1999), and a mixture of alfalfa hay and corn silage with 20 to 60% DM, respec- tively (Brown *et al*., 2000). South American studies conducted in Argentina used feedlot cattle fed with high-grain diets based on 70% DM dry-rolled corn grain and 30% DM pelleted sunflower meal (Geraci *et al*., 2012). In a Brazilian study, cattle were fed sorghum silage diets (40 to 70% DM) with concen- trates containing corn or soybean meal (30 to 60% DM, respectively; Pedreira *et al*., 2013).

In Europe, studies conducted in England used steers raised on forage-based diets with 70:30 (DM basis) grass hay: barley ratio (Lewis *et al*., 1996). In Spain, heifers received concentrate diets in which barley and corn represented 80% (Martın-Orue *et al*., 2000), 50% (Robles *et al*., 2007) and 60% (Falei- ro *et al*., 2011) of the TMR (DM basis). In Ireland, freshly cut herbage (*i.e.,* zero-grazed; Hart *et al*., 2009) or perennial ryegrass silage (Fitzsimons *et al*., 2013) was fed, with forage accounting for 90% of dietary DM. In France, bulls were offered grass hay, ground corn grain, and soybean meal (Doreau *et al*., 2011) accounting for 49, 63, and 16% of dietary DM, respectively. In Asian countries, Japanese studies used diets with 40% DM from forage, either from orchard grass or timothy hay, and concentrate from soy sauce cake (10 to 20%), with flaked-barley and corn (30 to 40% DM; Hosoda *et al*., 2012).

### 2.3 Dietary Compositions and Missing Values

Chemical composition of diets was recorded using the values given in each paper and ordered in Microsoft Excel© spreadsheet (Microsoft Office 2010, Seattle, Washington; App. Tables 12, 13, and 14). All diets were entered into the Cornell Penn Minor Dairy model (CPM-Dairy©; version 3.0, Bos- ton *et al*., 2000) to calculate the missing values not reported by the authors. In particular, many papers did not report sugar, starch, soluble fiber, NDF, and peNDF contents. When the DMI was reported as a metabolic DMI (MDMI), the values were converted into daily intake (as a percentage of DM in kg). In the CPM-dairy the physical effectiveness factor (pef) in the feed dictionary was obviously for dairy rations. Therefore, adjustments had to be made for all the dietary compositions assembled from the publications in DB (1) and (2) while it was entered into the CPM-dairy by modifying these values to the corresponding pef of the peNDF for beef cattle diets (NRC, 1984, 1996, 2000; Trenkle, 2002). For instance, when diets included steam-rolled barley in the original papers (*i.e.,* Paton *et al*. 2006; Beauchemin *et al*., 2007; Yang *et al*., 2010a; Holtshausen *et al*., 2011; Vyas *et al*., 2014a) it was by default with 40.0 pef in the CPM-dairy, which is not relevant for beef cattle diets (NRC, 2000). Thus it was replaced by barley grain, (75%) from the feed library listed in the CPM-dairy which had a default pef of 25.0.

### 2.4 Ruminal Fermentation Characteristics and Calculations

Mean RpH was recorded from each paper; however, there were differences among studies in the way the RpH had been measured. Ruminal pH measurements (RpHms) can be broadly classified as continuous wherein a complete pattern over 24-(h) is obtained from very frequent sampling or, usually, by using indwelling submersible pH electrodes. Alternatively, RpHms can be non-continuous, charac- terized by sampling rumen fluid once or at timed intervals for a portion of the 24-(h) cycle. Studies with continuous measurement of pH calculated mean RpH based as the average of the values recorded over 24-(h) (Krause *et al*., 1998; Cooper *et al*., 1999; Beauchemin *et al*.,2003; Ghorbani *et al*., 2002; Erick- son *et al*., 2003; Koenig *et al*., 2003; Schwartzkopf-Genswein *et al*., 2004; Bevans *et al*., 2005; Be- liveau and McKinnon, 2009; Wierenga *et al*., 2010; Yang *et al*., 2013; Holtshausen *et al*., 2011, 2013; Li *et al*., 2011, 2013; Moya *et al*., 2011; Van De Kerckhove *et al*., 2011; Walter *et al*., 2012; Hünerberg *et al*., 2013b; Koenig and Beauchemin, 2013; Schwaiger *et al*., 2013; Chung *et al*., 2013; Narvaez *et al*., 2014; Vyas *et al*., 2013, 2014a, 2014b). Recording frequency varied from 1 min (*e.g.*, Chung *et al*., 2013) to every 15 min (*e.g.*, Ghorbani *et al*., 2002). Both RpHms (*i.e.,* continuous *vs.* non-continuous) were tested combined (DB (1); n = 232; App. Tables 6, 12, and 13) or individually (DB (2); n = 95; App. Tables 7, 12 and 13) for developing mean RpH prediction models. The non-continuous studies measured RpH by ruminocentesis (e.g., Doreau *et al*., 2011), oral intubation (e.g., White *et al*., 1969; Horton *et al*., 1983), or via the rumen cannula by removing ruminal fluid either manually (e.g., Barajas and Zinn, 1998; Soita *et al*., 2003) or using a vacuum pump (e.g., Köster *et al*., 1996; Martın-Orue *et al*., 2000). In the case of ruminocentesis, sampling frequency was once, for oral intubation sampling frequency was infrequent (once; Horton *et al*., 1983; twice; White *et al*., 1969), and with cannulated cattle, various sampling intervals after feeding were used (Rumsey *et al*., 1970; Oltjen *et al*., 1971; Lee *et al*., 1982; Leventini *et al*., 1990; Zinn, 1990; Freeman *et al*., 1992; Murphy *et al*., 1994; Lewis *et al*., 1996; Zinn and Barajas, 1997 ; Olson *et al*., 1999; Pylot *et al*., 2000; Brown *et al*., 2000; Fellner *et al*. 2001; Beauchemin *et al*., 2001 ; Soita *et al*., 2003; Lardy *et al*., 2004; McGinn *et al*., 2004; Beauche- min and McGinn, 2005; Beauchemin and McGinn, 2006; Paton *et al*., 2006; Beauchemin *et al*., 2007, Robles *et al*., 2007; Hart *et al*., 2009; Yang *et al*., 2010a, 2010b; Faleiro *et al*., 2011; Van De Kerckhove *et al*., 2011; Geraci *et al*., 2012; Hosoda *et al*., 2012 ; Fitzsimons *et al*., 2013; Hünerberg *et al*., 2013a, 2013b; Pedreira *et al*., 2013; Friedt *et al*., 2014; He *et al*., 2014; Narvaez *et al*., 2014; Kerckhove *et al*., 2011; Yang *et al*., 2013 ; App. Tables 12 and 13).

The tVFAs concentrations were reported in most of the studies included in the databases (App. Ta- bles 4, 5, 12, and 13), except studies conducted by Horton *et al*. (1983), Zinn (1990), Zinn and Barajas (1997), Cooper *et al*. (1999), Brown *et al*. (2000), Erickson *et al*. (2003), Schwartzkopf-Genswein *et al*. (2004), Kerckhove *et al*. (2010), Holtshausen *et al*. (2013). When individual VFAs were expressed as concentration (*e.g.,* mgN/100 ml, mg/L, mg/dL, and NH3-N/100 ml, mg) the values were converted into molar proportions. Ammonia (Am) and Am nitrogen values were converted to Am concentration (m *M*). It is noteworthy that Baldwin *et al*., 1987a, b (BAL) equation could not be evaluated as there was no sufficient data (*i.e.,* lactic acid concentrations; n = 10) reported in the assembled papers necessary to run and compare the performance of BAL model with the other extant published equations.

### 2.5 Extant Prediction Equations

Published prediction models of the rumen functions have provided linear and polynomial (*i.e., * quadratic; ZB6) equations to predict the mean RpH. Only a few numbers of these models used beef cattle observations in the development process (Table 1). As noted previously, these models were based either on the peNDF of the diets (Pitt *et al*., 1996, PIT; Mertens, 1997, MER; Fox *et al*., 2004, FOX; Zebeli *et al*., 2006, ZB6 and Zebeli *et al*., 2008, ZB8) or the VFAs of the rumen (Tamminga and Van Vuuren, 1988, TAM; Lescoat and Sauvant, 1995, LES; Allen, 1997, ALL). Additionally, it should be noted that the term effective NDF (eNDF), rather than peNDF, was used in the original publication by Pitt *et al*. (1996). However, later versions of CNCPS version 5 (Fox *et al*., 2003, 2004), CNCPS version 6 (Tylutki *et al*., 2008) and CPM-Dairy version 3 (Boston *et al*., 2000) used peNDF to estimate ruminal pH in the equation from Pitt *et al*. (1996); thus similarly, eNDF was substituted for peNDF in PIT. Thereafter, using the 2 independent data sets (App. Tables 4, 5, 6, and 7) of beef cattle trials their predictive ability of mean RpH was tested over a wide range of feeding situations.

### 2.6 Development of new prediction equations

Statistical analyses were performed using the PROC MIXED regression model procedure of SAS (Littell *et al*., 2006) in JMP® (version. 11.0, 2013). Trial effect was considered not only as fixed but also as random because the data came from different trials, experimental conditions, and protocols. Multiple regression equations were developed by running iterations in the mixed model procedure, by adding all the ruminal fermentations variables (*i.e.,* AC, PR, BU and AM), dietary compositions and intake (*i.e.,* DMI, starch, ADF, etc.). Since the biological relationships are seldom linear over a wide range of values (Ellis *et al*., 2009); the quadratic and cubic terms and interactions of the nutrient varia- bles were also evaluated. To asses relationships between RpH and previous variables; a ‘stepwise’ method with a *P* -value of 0.10 and 0.05 to enter and remain, respectively, in the model and a maximum of three variables to enter the final equation were used. The backward elimination procedure for multi- ple regressions was used to attempt to determine independent variables that would improve predictions of mean RpH. Root mean square error (RMSE) was adjusted for random study effects and observations were weighted before performing each analysis, as described by St-Pierre (2001).

Collinearities which measure how highly correlated each independent variable is with the other predictors in the equation were evaluated by variance inflation factors (Belsley *et al*., 1980). Model performance was evaluated using Akaike's information criterion (AICc; Bozdogan, 1987) and Bayesian information criteria (BIC; Leonard and Hsu, 2001) as an indicator of the goodness of model fit. AICc select a model that produces the smallest expected discrepancy as follows:

illustration not visible in this excerpt

Where *m* is the maximum likelihood, δ is the chi-square criterion of the average log likelihood, p is the number of free parameters for each model, *i.e.,* a and b, and *N* is the sample size.

BIC are model-order selection criteria based on parsimony which favor simpler models by impos- ing penalty on models that include additional parameters (AlZahal *et al*., 2007). BIC combine both maximum and (log) maximum likelihood penalized with a term related to model complexity as follows:

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Where *J* ˆ is the maximum likelihood, *K* is the number of independent parameters in the model, and *N* is the sample size. When comparing models, a smaller numerical value of BIC indicates a better fit. Con- sequently, the best-model-fit to the observed data was chosen based on lowest AICc, BIC, and RMSE.

### 2.7 Models adequacy and evaluation

Model testing is often designed to demonstrate the rightness of a model as evidences to promote its acceptance and usability (Sterman, 2002). Thereafter, the robustness and reliability of the new equa- tions for predicting the mean RpH using the non-continuous and continuous RpHms from DB (1 and 2; App. Tables 4 and 5, respectively) were evaluated using a cross-validation analysis (CV, Picard and Cook, 1984). The data were split randomly into 5 subsets with all data from a particular study in the same subset. Each subset was in turn left out and equations were developed based on the remaining 4 subsets. The fitted equations had the same variables as those developed using PROC MIXED of SAS described previously. The resultant equation parameters were used to compute mean predicted RpH for the observations in the excluded subset, and the procedure was repeated for all subsets. Accuracy of models was assessed by computing the mean square prediction error (MSPE) as described by Bibby and Toutenburg (1977).

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Where I = 1, 2,..., *n*; *n* is the number of experimental observations; and Oi and Pi are the observed (measured) and predicted RpH values, respectively. The MSPE has limitation in assessing model per- formance in that it removes the negative sign and weighs the deviations by their squares, yielding more influence to larger deviations (Mitchell and Sheehy, 1997). Comparisons of model accuracy were based on the root of MSPE (RMSPE) and RMSPE as a percentage of the observed mean (%RMSPE) to pro- vide an indication of the overall error of prediction. Thus, mean square prediction error was decom- posed into error due to overall bias of prediction (ECT), error due to deviation of the regression slope from unity (ER), and error due to disturbance or random variation (ED) (Bibby and Toutenburg, 1977). These components partitioned into mean bias, slope bias, and dispersion proportions were calculated as:

illustration not visible in this excerpt

where [Abbildung in dieser Leseprobe nicht enthalten]are the averaged predicted and observed values, respectively; SP and So are the standard deviations (SD) of predicted and observed values, respectively; and r is the coefficient of correlation between predicted and observed values. The ECT represents the error in overall bias or central tendency indicates and indicates how the average of predicted values deviates from the average of observed val- ues; ER which is error due to regression, measures the deviation of the least squares regression coeffi- cient (r × So/SP) from unity, the value it would have been if the predictions were completely accurate; and, ED which is error due to disturbances, is the variation in observed values that is not accounted for by a least squares regression of observed on predicted values (Benchaar *et al*., 1998; Ellis *et al.,* 2010).

Adequacy of RpH predictability from equations developed in the cross-validation analysis was evaluated through Concordance correlation coefficient (CCC; Lin, 1989) as an indication of precision and the accuracy of predicted and observed values for the models. The CCC is a cross multiplication of ρ and C *b* and ranges from -1 to 1 where values closer to 1 indicate a more precise and accurate model.

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Where the first component is the Pearson correlation coefficient (ρ) that measures precision and the

second component (*C b*) is the bias correction factor that assesses model accuracy and is calculated as:

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If *C b* equals 1, this indicates that no deviation from a 45° slope had occurred. The multiplication of both values gives both precision and accuracy at the same time (Lin, 1989). The estimates (*v*) and (*µ*) measure the scale shift and the location shift relative to the scale or squared difference of the means relative to the product of two standard deviations, respectively (Kebreab *et al*., 2009; Ellis *et al*., 2006, 2009, 2010, 2011). Whereas, *v* value indicates the change in standard deviation, if any, between predicted and observed values (Ellis *et al*., 2009). A negative *µ* value indicates model overestimation (over-prediction), and a positive value indicates underestimation (under-prediction), of observed values. The calculated CCC parameters were verified using MedCalc® (version. 13.3, 2014, Ostend, Belgium).

The modeling efficiency statistic (MEF) was performed as discussed by Tedeschi (2006). This value is interpreted as the proportion of variation explained by the model-predicted (or simulated) value and thus, MEF may be used as a good indicator of goodness-of-fit, and is calculated as follows:

illustration not visible in this excerpt

Where: [Abbildung in dieser Leseprobe nicht enthalten] is the difference between observed and model-predicted values, [Abbildung in dieser Leseprobe nicht enthalten] is the mean

difference between observed (or measured) values. The closer the MEF is to 1, the more accurate the model is and vice-versa.

Models developed in this study and extant models were also evaluated using the coefficient of model determination (CD) as an indicator of the goodness of model fit (Ellis *et al*., 2009, 2011). The CD statistic is the ratio of the total variance of observed values to the square of the difference between model-predicted and mean of the observed data as described by Tedeschi (2006).

illustration not visible in this excerpt

where:[Abbildung in dieser Leseprobe nicht enthalten]is the difference between observed values and their mean, and [Abbildung in dieser Leseprobe nicht enthalten]is the *i* th modelpredicted values. The closer to unity, the better is the model prediction (Tedeschi 2006).

### 2.8 Residual analysis

An assessment of prediction bias is presented in the form of residual plots in which the residuals (observed minus predicted) were plotted against the predicted values (St-Pierre, 2003). This is because observed values contain natural variability whereas model-predicted values are deterministic with no random variation (Tedeschi, 2006; Piñeiro *et al*., 2008). Residuals were tested for normality using the UNIVARIATE procedure in SAS. Residual slopes were tested for significant difference from zero, an indication of heteroscedasticity for examination of any potentially confounding factors (Klop *et al*., 2013). The independent variable (predicted RpH) was centered around the mean predicted value before residuals were regressed on predicted values (St-Pierre, 2003). The significance of the intercept term at the mean value, a measure of the mean prediction bias, and the slope of this mean-centered regression, a measure of the linear prediction bias (St-Pierre, 2003). In addition, Mean centered bias and bias at the minimum and maximum values were determined as described by St-Pierre (2003).

## 3. Results

### 3.1.Descriptive Statistics of Literature Data

The collected data sets included a wide range of diet chemical compositions for DB (1) and (2) (App. Tables 4 and 5, respectively) and feed intakes (App. Tables 6 and 7, respectively). For example, the studies used in this analysis had mean forage content (% DM basis) of 34.8 for DB (1) and 26.9 for DB (2) and the DMI ranged from 1.13 to 14.3 kg/d for DB (1) and from 3.7 to 13.6 kg/d for DB (2). The combined concentrate (n = 215) and pasture-based (n = 17) diets used in this analysis (App. Table 11) had a mean RpH range of (5.06 to 7.09) for DB (1) (App. Table 4), whereas RpH ranged (5.06 to 7.09) from only concentrate-based, and (6.03 to 7.07) from only forage-based diets. In a similar range for DB (2), the combined concentrate (n = 89) and pasture-based (n = 6) diets had a mean RpH range of (5.5 to 6.81) (App. Table 5), whereas diets from only concentrate, and forage-based diets had a mean RpH range of (5.5 to 6.5) compared to (6.5 to 6.8), respectively. This RpH reflects the wide range in diets fed in beef production systems which is consistent with the expectations for cattle (5.7 to 6.9; n = 101; Morvay *et al*., 2011) and beef steers studies fed a TMR of concentrate and forage (90% DM basis) from 5.5 to 6.3 (n = 7; Estell and Galyean, 1985) and from 5.3 to 6.7 (n = 5; Peters *et al*., 1990).

Across-studies analysis of the DB (1) for linear (Lr), quadratic (Qr), and cubic (Cr) relationships is shown in (App. Tables 15.1, 15.2, 15.3, respectively) and visualized in (App. Table 15.4; n = 232). The strongest relationship considering linear and polynomial effects (*i.e.,* Cr and Qr) across studies was observed between mean RpH, and ruminal concentrations of PR and AC (r^{2} = -0.470 *vs. -* 0.570 Lr, 0.481 *vs. -* 0.591 Qr, and 0.490 *vs. -* 0.600 Cr) with ranging RMSE of 0.28 and 0.32, respectively. Simi- larily, between mean RpH and ADF, Forage, forage NDF, and starch, and molar concentrations of tVFAs (r^{2} = 0.330 *vs.* 0.410 Lr, 0.338 *vs.* 0.430 Qr, and 0.370 *vs.* 0.440 Cr) with a ranged RMSE of 0.32 and 0.36. These results support the fact that RpH fluctuations in beef cattle are certainly not ex- plained only by a linear response (Uhart and Carroll, 1967). Others reported the best variable for de- scribing RpH Lr was ADF, in beef steers fed a concentrate and pasture diets (r^{2} = 0.45; Estell and Galyean, 1985), and in cattle fed low fibre diets (r^{2} = 30%) using 23 published studies (Erdman, 1988).

The regression relationship for the DB (2): mean RpH = m + (b0), (b1), and (b2) x (*x*) where b0 is Lr, b1 is Qr, and b2 is Cr, and *x* = animal, dietary, and ruminal variables (App. Tables 16 and 16.1; n = 95). The best variables described Lr the mean RpH across the studies were from nadir RpH and dietary for- age (% DM, r^{2} = 0.673 and 0.784; RMSE = 0.47 and 0.34, respectively). Beside, the mean RpH across studies had Qr from molar proportions of AC and PR, dietary forage NDF, forage intake, and starch intake (% DM, r^{2} = 0.617 *vs.* 0.771; RMSE ranging 0.34 to 0.46). Moreover, A Cr of dietary ADF and forage NDF intake (DM basis) occurred, a finding similar to forage based studies in steers (Adams and Kartchner, 1984) and cattle (Stensig and Robinson, 1997). Nonetheless, the r^{2} values of these relation- ships (*P* < 0.001) were substantially higher than in DB (1) and explained 0.640 to 0.660 of the mean RpH variations, with RMSE of 0.33 to 0.51 for dietary forage NDF intake and ADF, respectively. Likewise, Cr between mean RpH and time pH < 5.8 (h) were observed, demonstrating that time when pH < 6.0 (h) could replace or complement mean RpH as descriptors of short-term ruminal acidity (Dra- gomir *et al*., 2008; Lechartier and Peyraud, 2011).

### 3.2.Correlation Analyses of Literature Data

Pearson's correlation test for DB (1) (App. Table 15.5) showed that mean RpH had a positive rela- tionship (*P* < 0.01; r^{2} = 0.200-0.680) with dietary forage, ADF, peNDF, NDF, forage NDF, lignin, sug- ar, ash, and ruminal concentrations of AC (as a proportion of tVFAs), and (*P* < 0.05; r^{2} = 0.040-0.150) soluble fiber and ruminal Am concentrations. A negative relationship (*P* < 0.01) was observed between DMI, PR, Starch, and tVFAs (simple correlations from [-] 0.330 to [-] 0.750). Similarly, positive corre- lations were observed for DB (2) with the previous variables with the exception of ash and Am (m *M*; App. Table 16.2). However, DB (2) had a stronger correlation range of 0.400 to 0.885. A negative cor- relation, as in DB (1), was observed in DB (2) with the exception of organic compounds (OC) such as organic matter (OM; *P* < 0.05), NFC, as well as metabolic DMI (MDMI; *P* < 0.01; App. Table 16.3). Again, this correlation magnitude (-0.274 to -0.851) was higher than within DB (1). In agreement with Kolver and De Veth (2002), RpH was positively related (*P* < 0.05; r^{2} < 0.15) to forage NDF and NDF, and negatively related (*P* = 0.001; r^{2} = 0.14) to NFC in pasture-fed cattle (90 % DM). Interestingly, NDF was not reliable for RpH predictions in pasture-based diets (90% DM; Kolver and De Veth, 2002). However, in concentrate fed diets (88% DM) forage NDF and rapidly degradable DM are good predictors of the mean RpH in cattle (*P* < 0.001; r^{2} = 0.64; n = 6; Lechartier and Peyraud, 2010).

### 3.3. Development of mean Rumen pH prediction models from all of the pH measurements observations

As described previously, the procedures in section 2.6 was applied on the DB (1) (App. Tables 4 and 6) and mixed regression analysis resulted in Table 2 as the best fit equations describing the mean RpH. The equations were developed in different categories (*i.e.,* Dietary compositions and VFA) and ranked according to the lowest AICc, BIC, and RMSE, and the highest R^{2} as listed in Table 2. For the VFA category, a multivariate Qr models (*P* < 0.01): Eq. (A) of BU (%), PR (%), and tVFAs (m *M*) ex- cept PR (%) were significant at *P* < 0.05, and Eq. (B) of starch (% DM, kg/d), PR (%), and BU (%) were significant at *P* < 0.01, except starch (% DM, kg/d) at *P* < 0.05. Dietary composition based models were developed either from their chemical proportions or from their intake, *i.e.* Eqs. (D) and (C), re- spectively. A multivariate Lr model: Eq. (D) of DMI (kg/d) and ADF (% DM) showed significance at *P * < 0.01 whereas, Qr model: Eq. (C) included forage NDF and NFC (% DM, kg/d; *P* < 0.01) and lignin (% DM, kg/d, *P* < 0.05). For each model, the intercept, slope, and the significance of the regression equation for the predicted mean RpH and their residuals are noted on the graphs (App. Figures 1 and 2).

Table 2. Ruminal pH empirical prediction model developed from *in-vivo* database (1) observations (n = 232)

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Figure 2. Comparison of predicted mean RpH values derived using the newly developed models shown in Table 2, with the measured mean RpHvalues derived from different RpH measurement techniques on DB (1) Collectively, all models predictabilities over DB (1) and (2) are shown in Figures 2 and 3, respec- tively. Evaluating the newly developed models (Table 2) was assessed as outlined previously in section 2.7. The equations were tested on DB (1) where they have been developed (n = 232). Tables 17 and 17.1, respectively provide summary statistics of models performance with models ranked using the highest CCC, as an indication of both precision and accuracy, and the lowest RMSPE, as an indicatio of prediction error of RpH. All models had a high accuracy for mean RpH predictions (C *b* = 0.95) for Eqs.

(B) and (D) with a tendency for under and over-prediction (*µ* = 0.10 and 0.20, respectively).

A negligible difference in the prediction accuracy (C *b* = 0.94) for Eq. (A) and (C) with a very high tendency for underprediction and slight overprediction of mean RpH was observed (*µ* = 0.29 and 0.08, respectively). The lowest RMSPE of all models were from Eqs. (A) and (B) with errors mainly due to random sources (ED of 84.4 to 89.8%) compared to 5.10 and 5.17 RMSPE from Eqs. (D) and (C) with also, errors mainly from random sources (97.0 to 98.2%, respectively). The MEF was the greatest of (0.57 *vs.* 0.66) for Eqs. (A) and (B) and the lowest of (0.39 *vs.* 0.40) for Eqs. (C) and (D). The VFAs and dietary models of Eqs. (A) and (B) when applied on DB (2), where the mean RpH was continuous- ly measured (n = 95), had superiority in terms of CCC over the rest of the tested models. Models per- formances are ranked, as noted previously, using highest CCC and lowest RMSPE (Tables 17.2 and 17.3, respectively). There was a significant (*P* < 0.01) improvement in mean RpH predictions for all models in terms of R^{2} and RMSE (App. Figures 1 and 2). In addition, Eqs. (B) and (D) showed a lower RMSPE (2.93 and 3.06% of MSPE) with (72.2 and 82.8%) errors from random variations, respectively.

For all models applied on DB (1) there was neither linear bias (*i.e.,* slope) nor mean bias except mean bias (*i.e.,* intercept) (*P* < 0.001) for Eq. (A) and (B) of -0.10 and -0.07 over the range of RpH pre- diction, respectively. At the minimum, RpH prediction of 5.46 for Eq. (B) the bias was -0.48, and at the minimum RpH prediction of 5.41 for Eq. (A) the bias was -0.62. The maximum mean RpH prediction for Eqs. (A) and (B) was 6.89 with bias of 0.68, and 6.72 with a bias of 0.78, respectively. The applica- tion of the previous models on DB (2) for prediction biases showed a similar performance over the range of RpH prediction. At the minimum, RpH prediction of 6.72 for Eq. (B) the bias was -0.63, and of 6.84 for Eq. (A) the bias was -0.73. The maximum prediction for Eqs. (A) and (B) was 6.84 with 0.54 bias, and 6.72 with 0.58 bias, respectively. The CD from the lowest to the highest varied from (0.89 *-* 1.39) for Eq. (B), (0.91 to 1.39) for Eq. (A), (1.26 to 1.77) for Eq. (D), and (1.44 to 1.95) for Eq. (C) when the models were tested on DB (2) and (1), respectively (App. Figures 1 and 2). The R^{2} values for mean RpH predictions from the highest to the lowest are ranged between (0.69 to 0.74) for Eq. (B), (0.63 to 0.73) for Eq. (A), (0.42 to 0.70) for Eq. (D), and (0.39 to 0.67) for Eq. (C) when the models were tested on DB (1) and (2), respectively.

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Figure 3. Comparison of predicted mean RpH values derived using the newly developed models shown in Table 2, with the measured mean RpHvalues derived from different RpH measurement techniques on DB (2)

### 3.4. Development of mean Rumen pH prediction models from continuously measured observations

The DB (2) included observations (n = 95) of mean RpHms in a continuous patterns over 24-(h). Of the dependent variables (App. Tables 5 and 7) considered as well as their squared values (*i.e.,* quad- ratic effect), the same procedure and selection criteria as mentioned previously were used and resulted in the best-fit models describing the mean RpH (Table 3). Only Am (m *M*, *P* < 0.05) and AC (%, *P* < 0.01) responded in a (Cr) and met the criteria to enter and remain (*P* = 0.25 and *P* = 0.05, respectively) in the models for Eqs. (F) and (G). Similarly, combining dietary and ruminal variables resulted in Eq. (I) for dietary intake and VFA, and Eqs. (E) and (L) which represented the diet and VFA. The previous Lr models that considered dietary forage proportions (DM basis) and ruminal AC (%) showed signifi- cance at *P* < 0.01 whereas; ruminal Am (m *M*) and BU (%), and dietary OM, peNDF, and starch (% DM) showed significance at *P* < 0.05. The dietary intake variables (% DM, kg/d) resulted in a Qr mod- el for Eq. (J) and Lr model for Eq. (K). The parameters of these models included EE, forage (*P* < 0.01) and sugar (*P* < 0.05). For the dietary compositions (% DM), Lr models Eqs. (H), (M), (N), (O), and Qr

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Table 3. Ruminal pH empirical prediction model developed from *in-vivo* database (2) observations (n = 95)

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models Eq. (P) were the best fit for predicting mean RpH. All of the Lr models included forage, NDF, peNDF (*P* < 0.01) and starch (*P* < 0.05) whereas; Qr models included only NDF and starch (*P* < 0.05).

The performance of the previous models when applied on DB (2) is provided in Table 18. The analysis revealed that from all of the tested models, the highest CCC of 0.90 was from Eqs. (E), (F), and (H) with ρ and C *b* of 0.91 and 1.0, respectively except Eq. (I) with a CCC of 0.88. The lowest RMSPE (2.18 to 2.54%) was from Eqs. (E), (F), (G), (H), and (I) with errors mainly due to random sources (ED = 96.6 to 99.6%) and the lowest overall bias (ECT = 0.20%) and linear bias (ER = 0.02%) from Eq. (H) and (F) respectively (App. table 18.1). The Eq. (I) and (E) had a tendency for slight un- der-prediction of mean RpH (*µ* = 0.04 and 0.07, respectively) whereas, Eqs. (F) and (G) had a tendency for slight over-prediction of mean RpH (*µ* = 0.03 and 0.04, respectively). Surprisingly, Eq. (H) showed almost no inclination (*µ* = 0.02) for mean RpH predictions. All predictions of the models shown in Ta- ble 3, when applied against DB (1) and (2) are provided in Figures 4 and 5, respectively.For all tested models on DB (2), MEF of 0.81 for Eqs. (F) and (H), and of 0.82 for Eq. (E) was the highest. When models being tested on DB (1); Eqs. (F), (G), and (H) had the highest CCC (0.61 to 0.64), C *b* (0.96 to 0.97), and ρ (0.63 to 0.66) (App. Table 18.2). The lowest RMSPE (5.32 to 5.56%) with errors mainly from random variations (ED = 93.7 to 98.5%) and lowest overall prediction error (0.32%) was observed from Eq. (G) (App. Table 18.3).

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Figure 4. Observed *versus* predicted mean RpH from the developed models shown in Table 2 when tested on DB (1), and the models are written in a descending order, *i.e.* in the legend, according to the priority of appearance from top to bottom Prediction biases of the models for mean RpH from pooled DB (1) and (2) are presented in Table 18.4. All of the tested models for DB (2) showed neither significant mean nor linear bias except Eq. (L) had a significant *P* < 0.001 mean RpH prediction linear bias (-0.99) of 4.83 at the minimum, and (0.86) of 6.69 at the maximum, and mean bias of 0.27 (App. Figure 3.5). For DB (1) there was a significant mean bias for all models except Eqs. (G) and (F) (*P* = 0.403 and *P* = 0.422, respectively; App. Figure 3.5), and a significant linear bias for all models (App. Figures 3.3 and 3.7) except for Eqs. (G), (M), (N), (O), and (P) (App. Figures 3.9 and 3.11). The magnitude of linear bias was from (-0.60 to -1.91) at 23 the minimum of (4.80 to 5.72) and from (0.32 to 1.89) at the maximum of (6.65 to 7.93). Overall MEF of (0.81 to 0.82) for all models tested on DB (2) was the highest for Eqs. (E), (F), and (H), intermediary (0.60 to 0.77) for Eqs. (I), (G), (J), (K), and (M), and the lowest of (-1.08 to 0.51) for the rest of the models. The models notably had a very low performance with maximum MEF of (0.43) for Eq. (G), intermediary MEF of (0.34 to 0.37) for Eqs. (F), (H), and (M), and the lowest MEF of (-0.19 to 0.27) for the rest of the models when they have been applied on DB (1). A remarkable improvement for mean RpH predictions was explained from DB (2). The R^{2} values from the highest to the lowest ranged be- tween (0.39 to 0.82) for Eq. (E), (H), and (F), (0.44 to 0.77) for Eqs. (I) and (G), and (0.14 to 0.67) for Eqs. (J), (K), (M), (N), (P), (O), and (L) for the tested models either on DB (1) or DB (2), respectively (App. Figures 3.2, 3.4, 3.6, 3.8 and 3.10). The CD varied from (0.27 to 1.09) for Eqs. (L) and (I), (1.10 to 1.79) for Eqs. (E), (H), (F), (G), (J), and (K), and (1.63 to 2.51) for Eqs. (M), (N), (P), and (O) from the lowest to the highest when being tested on DB (2) and (1) independently.

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Figure 5. Observed *versus* predicted mean RpH from the developed models shown in Table 2 when tested on DB (2), and the models are written in a descending order, *i.e.* in the legend, according to the priority of appearance from top to bottom

### 3.5.Evaluation of extant Rumen pH prediction models

App. Tables 19, 19.1, 19.2, and 19.3 provide summary statistics of model performance tested on DB (1) and (2) for RpH predictions, with models ranked using the highest CCC and RMSPE. Observed *versus* predicted RpH for tested models (individually) on DB (1) and (2) are shown in App. Figures 4, 4.2, and 4.4. All of the models when tested over DB (1) and (2) are provided in Figures 6 and 7, respec- tively. The models were divided based on tVFAs (ALL, LES, and TAM), or based on peNDF with beef (FOX and PIT), and dairy (MER, ZB6, and ZB8) observations with residuals plotted against centered predicted RpH values for tested models on DB (1) and (2) are shown in App. Figures 4.1, 4.3 and 4.5. The regression equation for predicted mean RpH and their residuals are noted on the Figures. Analysis of the residuals and prediction biases for tested models on DB (1) and (2) is given in App. Table 19.4.

#### 3.5.1 Performance of the tested models against all the different rumen pH measurements . observations

Tested models (n = 232 observations) with greatest accuracy for mean RpH prediction were LES and and TAM (C *b* = 1 and 0.99, respectively), with a tendency for underprediction with LES (*µ* = 0.06) and over-prediction with TAM (*µ* = 0.11). Both of these models predict RpH from VFAs concentration. Of the models that are based on peNDF, PIT and FOX were most accurate (C *b* = 0.95 and 0.96) both with a slight tendency to under-predict mean RpH (µ = 0.09 and 0.08, respectively). The ZB8 and ZB6 models had intermediate accuracy (0.76 and 0.73, respectively) but substantially underpredicted mean RpH (*µ* = 0.43 and 0.82, respectively). The least accurate models were ALL (based on VFA) and MER (based on peNDF) (0.58 and 0.56, respectively), and both substantially under-predicted RpH (*µ* = 0.49 and 1.01, respectively). All models had similar precision (ρ of 0.57 to 0.58), except MER and ZB which were considerably less precise (ρ = 0.47 and 0.24, respectively). Overall MEF was greatest for PIT and FOX (0.30 and 0.29, respectively), intermediate for ALL, LES, and ZB8 (0.20, 0.21, and 0.24, respec- tively) and least for MER, TAM, and ZB6 (- 4.53, 0.15, and - 0.88, respectively).

The RMSPE were relatively similar for all models (5.87 to 6.51%), except for ALL (9.64%) and MER (16.5%). The error associated with prediction using PIT and FOX was mainly from random sources (ED = 95.2 and 95.0%, respectively) with the remaining error mostly due to deviation of the regression slope from unity (ER = 3.94 and 4.37%, respectively), as there was very little overall bias (ECT = 0.90 and 0.62%, respectively). The error associated with using LES and TAM was also mostly random (ED of 77.5 to 83.3%), with very little overall bias (ECT = 0.40 and 1.38%, respectively), but there was notable error due to deviation of the regression slope from unity (16.3 and 21.1%, respective- ly). For ZB8 and ALL, although the error was mainly from random sources (86.9 and 82.7%, respec- tively), the remaining error was due to bias (ECT = 12.7 and 10.8%, respectively) and, for ALL, devia- tion of the regression slope from unity (ER = 6.57%). Errors for the least accurate and precise models, MER and ZB6, were due to a combination of sources: random (ED = 14.2 and 50.0%), bias (ECT = 38.3 and 30.6%), and deviation of the regression slope from unity (ER = 47.5 and 19.2%, respectively).

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Figure 6. Comparison of predicted mean RpH values derived using the models proposed by ALL, FOX, LES, MER, PIT, TAM, ZB6, and ZB8 tested on DB (1), with measured mean RpH derived from different RpH measurement techniques, and models are written in a descending order, *i.e.* in the legend, according to the priority of appearance from top to bottom

There was linear bias for all models (*P* < 0.002) except ZB8 (*P* = 0.343) over the range of RpH prediction. Of the models with linear bias for mean RpH prediction, those of ALL (*P* = 0.021) and FOX (*P* = 0.003) had the least bias. At the minimum RpH prediction of 5.82 for the ALL model, the bias was -0.30 and at the minimum prediction of 5.61 for FOX, the bias was -0.44. For ALL the maximum pre- diction was 6.56 with a bias of 0.16, while for FOX the maximum prediction was 6.46 with a bias of 0.39. The highest magnitude of linear bias (*P* < 0.001) for mean RpH prediction occurred for MER with a minimum prediction of 3.46 and a bias of -1.09 and TAM with a minimum prediction of 5.62 and bias of -0.88. For the MER and TAM models, the maximum prediction was 6.48 with bias of 1.92 and 7.73 with a bias of 0.47, respectively. There was mean bias, *i.e,* intercept, for FOX, TAM, MER, ZB6, and ZB8 ranging from 0.10 to 0.72. In comparison, mean bias of the remaining models of ALL, PIT, and LES (ranging from -0.04 to 0.034) was considerably lower than the SD of the predicted mean RpH. The models CD were the highest for ALL and ZB8 (ranging from 2.56 to 3.92), intermediary (ranging from 0.97 to 1.13) for LES, TAM, and ZB8, the least (ranging from 0.21 to 0.41) for FOX, MER, and PIT.

#### 3.5.2Performance of the tested models against continuously measured rumen pH observations

The FOX, PIT, and ZB8 models had the highest CCC (ranging from 0.66 to 0.72) of all tested models (n = 95), followed by LES and TAM (ranging from 0.59 to 0.61), and the least CCC (ranging from 0.29 to 0.40) for ALL, MER and ZB6. There was a tendency for a slight over-prediction of the mean RpH from LES, PIT, FOX, and TAM (*µ* = 0.06, 0.12, 0.15, and 0.27, respectively). Besides, a slight under-prediction of the mean RpH from ALL and ZB8 (*µ* = 0.11 and 0.18, respectively) whereas, ZB6 and MER tended to highly under-predict the mean RpH (*µ* = 0.82 and 1.28, respectively). The ZB8, PIT, and FOX had the least RMSPE (3.61, 3.84, and 3.92%, respectively) with errors mainly from random sources (ED ranging from 83.4 to 94.8%). The ALL, LES, and TAM had intermediate RMSPE (4.12, 4.41, and 4.77%, respectively) with the errors mainly due to random variations (ED ranging from 68.1 to 91.5%) and the highest errors due to linear bias from LES and TAM (ER = 19.9 and 23.5%, respectively). The highest RMSPE of all models were from ZB6 and MER (7.09 and 12.9%, respective- ly) with the highest errors of 45.5% from ZB6 from random sources and 57% overall biases from MER.

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Figure 7. Comparison of predicted mean RpH values derived using the models proposed by ALL, FOX, LES, MER, PIT, TAM, ZB6, and ZB8 tested on DB (2), with measured mean RpH derived from continuous RpH measurement techniques, and models are written in a descending order, *i.e.* in the legend, according to the priority of appearance from top to bottom

The MEF was the highest of (0.51) for ZB8, intermediary (ranging from 0.42 to 0.44, respectively) for FOX and PIT, and the lowest for ALL, LES, MER, TAM, and ZB6 (ranging from -5.31 to 0.31). The models CD was the lowest (0.12 to 0.59, respectively) for MER and ZB6, intermediately (ranging from 0.81 to 1.04) for FOX, LES, PIT, and TAM, and the highest (2.17 and 6.85, respectively) for ZB8 and ALL. There was linear bias for all models except ZB8 (*P* = 0.281) over the range of RpH predic- tion. Of the models with linear bias for mean RpH prediction, those of FOX (*P* = 0.001) and PIT (*P* = 0.002) had the least bias. At the minimum RpH prediction of 5.52 for FOX, the bias was -0.37 and at the minimum prediction of 5.55 for PIT, the bias was -0.38. For FOX the maximum prediction was 6.46 with a bias of 0.55, while for PIT maximum prediction was 6.46 with a bias of 0.52. The highest magnitude of linear bias (*P* < 0.001) for mean RpH prediction occurred for LES with a minimum pre- diction of 5.15 and a bias of -1.21, and TAM with a minimum prediction of 5.15 and a bias of -1.30.

For the LES and TAM models, the maximum prediction was 7.33 with bias of 0.97, and 7.49 with bias of 1.04, respectively. There was a mean bias for ALL, MER, ZB6, and ZB8 (*P* < 0.001). For these models the mean bias (ranging from 0.31 to 1.61). In comparison, the mean bias of the remaining mod- els (ranging from 0.56 to 0.74) was considerably lower than the SD of the predicted mean RpH.

## 4. Discussion

There was considerable variation among the collected studies, in the analysis realised above, in terms of the way the mean pH was measured. Both the continuous and non-continuous methods were used to measure RpH and the frequency of pH sampling within the studies that used non-continuous methods also varied considerably. This is logical since the objectives of these studies focused on pre- dicting the mean ruminal pH, but their average pH was determined over a particular sampling duration depending on the study conditions, *i.e.* assumptions, hypotheses and objectives. Hence it is not surpriz- ing that sampling frequency and duration ranged considerably amongst studies. For example, in studies that used continuous pH recording, sampling was frequent and the entire 24 h period was represented, whereas for studies that used non-continuous measurements, sampling frequency was relatively low and in most cases samples were not taken over a full 24 h period. Futhermore, no correction was made to account for potential differences in the pH due to sampling method or site. As a consequence, pH determined in ruminal fluid obtained by ruminocentesis is about 0.3 pH units lower than for fluid col- lected through a rumen cannula (Garrett *et al.,* 1999). Additionally, samples collected via an oral probe can be contaminated with saliva, inflating the pH value (Nocek, 1997). However, the insertion depth when using an oral probe is important to obtain representative rumen fluid samples (Shen *et al.* 2012). Therefore, the lack of a common standardized measurement for determining mean pH introduced con- siderable variation into the observed values of RpH, which would have increased the errors associated with prediction, even if this systematic bias is taking into account by a constant term in our models.

### 4.1.Ruminal pH Prediction from the extant published models

Of the extant models evaluated and ranked for mean RpH predictions, the INRA model (LES), fol- lowed by TAM, were the most accurate and precise models for beef cattle in DB (1) and (2). Both models are based on VFAs. Overall goodness of fit of LES and TAM were generally similar; however, both substantially deviated from the x=y line, with underestimation at low RpH and overestimation at high RpH.

**[...]**

^{1} Notations for each model corresponding to the intended equation.

^{2} C: country in which the model was developed: US; United States, GR; Germany, NL; Netherlands, FR; France.

^{3} Number of studies used to model ruminal pH from the original paper.

^{4} RMSE: root mean square error from the original paper.

^{5} R^{2}: coefficient of determination from the original paper.

^{6} Database: animal type used in modeling ruminal pH.

^{7} *n*: number of observation treatment means used to model ruminal pH.

^{8} Data is not available from the original paper.

^{1} Source data were treatment means from the experiments of: White *et al*., 1969; Rumsey *et al*., 1970; Oltjen *et al*., 1971; Lee *et al*., 1982; Horton *et al*., 1983; Leventini *et al*., 1990; Zinn, 1990; Freeman *et al*., 1992; Murphy *et al*., 1994; Köster *et al*., 1996; Lewis *et al*., 1996; Zinn and Barajas, 1997; Barajas and Zinn, 1998; Krause *et al*., 1998; Cooper *et al*., 1999; Olson *et al*., 1999; Brown *et al*., 2000; Martın-Orue *et al*., 2000; Pylot *et al*., 2000; Fellner *et al*., 2001; Beauchemin *et al*., 2001, 2003, 2007; Ghorbani *et al*., 2002; Erickson *et al*., 2003; Koenig *et al*., 2003; Soita *et al*., 2003; Lardy *et al*., 2004; McGinn *et al*., 2004; Schwartzkopf-Genswein *et al*., 2004; Beauchemin and McGinn, 2005, 2006; Bevans *et al*., 2005; Paton *et al*., 2006; Robles *et al*., 2007; Hart *et al*., 2009; Beliveau and McKinnon, 2009; Wierenga *et al*., 2010; Yang *et al*., 2010a, 2010b, 2013; Doreau *et al*., 2011; Faleiro *et al*., 2011; Holtshausen *et al*., 2011, 2013; Li *et al*., 2011, 2013; Moya *et al*., 2011; Van De Kerckhove *et al*., 2011; Geraci *et al*., 2012; Hosoda *et al*., 2012; Walter *et al*., 2012; Fitzsimons *et al*., 2013; Hünerberg *et al*., 2013a, 2013b; Koenig and Beauchemin, 2013; Chung *et al*., 2013; Pedreira *et al*., 2013; Schwaiger *et al*., 2013; Vyas *et al*., 2013, 2014a, 2014b; Friedt *et al*., 2014; He *et al*., 2014; and Narvaez *et al*., 2014.

^{2} Equations are ranked with the lowest RMSE, AICc, and BIC and the highest R^{2} for each category.

^{3} AICc: Akaike’s information criterion, a measure of the relative goodness of fit of the model.

^{4} BIC: Bayesian information criteria are model-order selection criteria based on parsimony.

^{5} RMSE: Root Mean Square Error.

^{6} Propionate-quadratic: is equal to propionate (mol/100 mol) × propionate (mol/100 mol).

^{7} Butyrateate-quadratic: is equal to butyrate (mol/100 mol) × butyrate (mol/100 mol).

^{8} Starch-quadratic: is equal to starch (% diet DM) × starch (% diet DM).

^{9} Lignin-quadratic: is equal to lignin (kg d-^{1}, % diet DM) × lignin (kg d-^{1}, % diet DM).

**Statistical significance at *P* < 0.01.

*Statistical significance at *P* < 0.05.

^{1} Source data were treatment means from the experiments of : Krause *et al*., 1998; Cooper *et al*., 1999; Beauchemin *et al*.,2003; Ghorbani *et al*., 2002; Erickson *et al*., 2003; Koenig *et al*., 2003; Schwartzkopf-Genswein *et al*., 2004; Bevans *et al*., 2005; Beliveau and McKinnon, 2009; Wierenga *et al*., 2010; Yang *et al*., 2013; Holtshausen *et al*., 2011, 2013; Li *et al*., 2011, 2013; Moya *et al*., 2011; Van De Kerckhove *et al*., 2011; Walter *et al*., 2012; Hünerberg *et al*., 2013b; Koenig and Beauchemin, 2013; Schwaiger *et al*., 2013; Chung *et al*., 2013; Narvaez *et al*., 2014; Vyas *et al*., 2013, 2014a, 2014b.

^{2} Equations are ranked with the lowest RMSE, AICc, and BIC and the highest R^{2} for each category.

^{3} AICc: Akaike’s information criterion, a measure of the relative goodness of fit of the model.

^{4} BIC: Bayesian information criteria are model-order selection criteria based on parsimony.

^{5} RMSE: Root Mean Square Error.

^{6} Ammonia-cubic: is equal to ammonia (m *M*) × ammonia (m *M*) × ammonia (m *M*).

^{7} Acetate-cubic: is equal to acetate (mol/100 mol) × acetate (mol/100 mol) × acetate (mol/100 mol).

^{8} Forage-quadratic: is equal to forage (kg d-^{1}, % diet DM) × forage (kg d-^{1}, % diet DM).

^{9} Sugar-quadratic: is equal to sugar (kg d-^{1}, % diet DM) × sugar (kg d-^{1}, % diet DM).

^{10} NDF-quadratic: is equal to NDF (% diet DM) × NDF (% diet DM).

^{11} Starch-quadratic: is equal to starch (% diet DM) × starch (% diet DM).

**Statistical significance at *P* < 0.01.

*Statistical significance at *P* < 0.05.

- Quote paper
- M.Sc. Management of Animal Resources and Sustainable Development in Agriculture Mohamed Sarhan (Author), 2015, Prediction of Ruminal pH for Beef Cattle. A Physiological Modelling Approach, Munich, GRIN Verlag, https://www.grin.com/document/293688

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